Q.1 The LCM and the HCF of the numbers 28 and 42 are in the ratio : 6 : 1 2 : 3 3 : 2 7 : 2
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Q.2 If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two num- bers is 5 15 45 270
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Q.3 The ratio of two numbers is 4 : 5 and their L.C.M. is 120. The numbers are 30, 40 40, 32 24, 30 36, 20
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Q.4 Three numbers are in the ratio 2 : 3 : 4 and their H.C.F. is 12. The L.C.M. of the numbers is 144 192 96 72
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Q.5 Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is 100 80 60 50
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Q.6 Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is 21 24 28 84
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Q.7 Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is 48 42 36 24
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Q.8 The ratio of the sum to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller number is : 20 16 12 8
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Q.9 Two numbers are in the ratio 3 : 4. The product of their H.C.F. and L.C.M. is 2028. The sum of the numbers is 68 72 86 91
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Q.10 The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is 28 32 40 64
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Q.11 The ratio of two numbers is 4 : 5 and their H.C.F. is 8. Then their L.C.M. is 130 140 150 160
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Q.12 The ratio of two numbers is 3 : 4 and their HCF is 5. Their LCM is: 10 60 15 12
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Q.13 Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are 12, 24, 36 5, 10, 15 4, 8, 12 10, 20, 30
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Q.14 If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two num- bers is yz xz/y xy/z xyz
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Q.15 The H.C.F. and L.C.M. of two numbers are 21 and 84 respec- tively. If the ratio the two num- bers is 1 : 4, then the larger of the two numbers is 12 108 48 84
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Q.16 The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers ? 8 and 6 8 and 10 2 and 4 6 and 4
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Q.17 The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is 10 46 70 90
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Q.18 Two numbers, both greater than 29, have HCF 29 and LCM 4147. The sum of the numbers is 966 696 669 666
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Q.19 The sum of the H.C.F. and L.C.M of two numbers is 680 and the L.C.M. is 84 times the H.C.F. If one of the number is 56, the other is : 84 12 8 96
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Q.20 The sum of two numbers is 84 and their HCF is 12. Total num- ber of such pairs of number is 2 3 4 5
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Q.21 The sum of a pair of positive in- teger is 336 and their H.C.F. is 21. The number of such possi- ble pairs is 2 3 4 5
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Q.22 The sum of two numbers is 45.Their difference is 1/9 of their sum. Their L.C.M. is 200 250 100 150
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Q.23 The H.C.F. of two numbers, each having three digits , is 17 and their L.C.M. is 714. The sum of the numbers will be 289 391 221 731
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Q.24 The product of the LCM and the HCF of two numbers is 24. If the difference of the numbers is 2, then the greater of the number is 3 4 6 8
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Q.25 The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there? 1 2 3 0
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Q.26 The LCM of two numbers is 12 times their HCF. The sum of the HCF and the LCM is 403. If one of the number is 93, then the other number is 124 128 134 138
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Q.27 Sum of two numbers is 384. H.C.F. of the numbers is 48. The difference of the numbers is 100 192 288 336
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Q.28 The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is 2/35 3/25 4/35 2/25
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Q.29 L.C.M. of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers ? 140 80 60 70
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Q.30 Three numbers which are co- prime to one another are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is 75 81 85 89
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Q.31 The sum of two numbers is 36 and their H.C.F. is 4. How many pairs of such numbers are pos- sible ? 1 2 3 4
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Q.32 If the HCF and LCM of two con- secutive (positive) even numbers be 2 and 84 respectively, then the sum of the numbers is 30 26 14 34
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Q.33 The LCM of two positive integers is twice the larger number. The difference of the smaller number and the GCD of the two numbers is 4. The smaller number is : 12 6 8 10
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Q.34 The L.C.M. of two numbers is 20 times their H.C.F. The sum of H.C.F. and L.C.M. is 2520. If one of the number is 480, the other number is : 400 480 520 600
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Q.35 The LCM of two numbers is 44 times of their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the oth- er number is 1100 975 900 800
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Q.36 If A and B are the H.C.F. and L.C.M. respectively of two al- gebraic expressions x and y, and A + B = x + y, then the value of A 3 + B 3 is x qube- y qube x qube y qube x qube + y qube
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Q.37 HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is : 70 77 63 56
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Q.38 The number between 3000 and 4000 which is exactly divisible by 30, 36 and 80 is 3625 3250 3500 3600
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Q.39 Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is 21 22 18 24
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Q.40 The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 is 9828 9288 9882 9928
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Q.41 A number x is divisible by 7. When this number is divided by 8, 12 and 16. It leaves a remain- der 3 in each case. The least value of x is: 148 149 150 147
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Q.42 Let x be the smallest number, which when added to 2000 makes the resulting number di- visible by 12, 16, 18 and 21. The sum of the digits of x is 7 5 6 4
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Q.43 The smallest five digit number which is divisible by 12,18 and 21 is : 10224 30256 10080 50321
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Q.44 A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is 1451 1641 1712 1523
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Q.45 The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is 4023 4032 4302 4203
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Q.46 If the product of three consecu- tive numbers is 210 then sum of the smaller number is 3 4 5 11
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Q.47 The LCM of two multiples of 12 is 1056. If one of the number is 132, the other number is 12 72 96 132
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Q.48 The least number to be sub- tracted from 36798 to get a num- ber which is exactly divisible by 78 is 18 60 38 68
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Q.49 Find the least multiple of 23, which when divided by 18, 21 and 24 leaves the remainder 7, 10 and 13 respectively. 3013 3024 3002 3036
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Q.50 The greatest number, that divides 122 and 243 leaving respectively 2 and 3 as remainders, is 12 24 30 120
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Q.51 If P = 23 . 310 . 5 ; Q = 25.3.7, then HCF of P and Q is : 2.3.5.7 3.23 22 . 37 25 . 310. 5 . 7
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Q.52 A fraction becomes 1⁄6 when 4 is subtracted from its numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes 1⁄3 . Then, the LCM of the numerator and denominator of the said fraction, must be 14 350 5 70
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Q.53 The HCF (GCD) of a, b is 12, a, b are positive integers and a > b > 12. The smallest values of (a, b) are respectively 12, 24 24, 12 24, 36 36, 24
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Q.54 The number of pair of positive integers whose sum is 99 and HCF is 9 is 2 3 4 5
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