The LCM of two numbers is 441 and their HCF is 21 If one of the number is 63 find the other number

Last updated - October 16, 2022

Answer: HCF = 9 and LCM = 504

Step by step solution:

Contents:

Given numbers = 63 and 72

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 63:
63 = 3 × 21
= 3 × 3 × 7

Prime Factorization of 72:

HCF of 63 and 72 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 3, 3

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

HCF = 3 × 3
= 9

∴ HCF(63, 72) = 9

LCM of 63 and 72 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 3 × 3 × 7 × 2 × 2 × 2
= 504

∴ LCM(63, 72) = 504

Division Method:

HCF of 63 and 72 by division method:

In the above division, the last divisor is 9.

Hence the HCF(GCD) of 63 and 72 = 9

∴ HCF(63, 72) = 9

LCM of 63 and 72 by division method

∴ LCM(63, 72) = 504

HCF of 63 and 72 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 63:

13792163

Factors of 72:

12346891218243672

The greatest common factor in the above lists will be the HCF of the given numbers.

9 is the greatest factor which is common in the above lists.

∴ HCF(63, 72) = 9

LCM of 63 and 72 by Listing Multiples Method:

To find LCM by listing multiples method we will list down the multiples of given numbers.

Multiples of 63:

63126189252315378441504567630

Multiples of 72:

72144216288360432504576648720

The lowest common multiple in the above lists will be the LCM of the given numbers.

504 is the lowest multiple which is common in the above lists.

∴ LCM(63, 72) = 504

If the HCF of two numbers is 9 and their product is 4536, what is their LCM?

If the LCM of two numbers is 504 and their product is 4536, what is their HCF?

HCF and LCM of two numbers is 9 and 504 respectively. If one number is 72, what is the other number?

Let other number be x.
Given:
HCF(72, x) = 9
LCM(72, x) = 504
∵ HCF × LCM = product of numbers
∴ 9 × 504 = 72 × x
∴ 4536 = 72x
∴ 4536⁄72 = x
∴ x = 63
Hence, the other number is 63.

Last updated - March 13, 2022

Answer: HCF = 21 and LCM = 63

Step by step solution:

Contents:

Given numbers = 21 and 63

To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers.

Prime Factorization of 21:
21 = 3 × 7

Prime Factorization of 63:

HCF of 21 and 63 by prime factorization method:

Common factors in above prime factors of given numbers are underlined.

Common prime factors = 3, 7

Now we have to multiply these common prime factors to obtain the HCF of given numbers.

HCF = 3 × 7
= 21

∴ HCF(21, 63) = 21

LCM of 21 and 63 by prime factorization method:

Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers.

In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers.

Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table.

LCM = 3 × 3 × 7
= 63

∴ LCM(21, 63) = 63

Division Method:

HCF of 21 and 63 by division method:

In the above division, the last divisor is 21.

Hence the HCF(GCF) of 21 and 63 = 21

∴ HCF(21, 63) = 21

LCM of 21 and 63 by division method

∴ LCM(21, 63) = 63

HCF of 21 and 63 by Listing Factors Method:

To find HCF by listing factors method we will list down all the factors of the given numbers.

Factors of 21:

13721

Factors of 63:

13792163

The greatest common factor in the above lists will be the HCF of the given numbers.

21 is the greatest factor which is common in the above lists.

∴ HCF(21, 63) = 21

LCM of 21 and 63 by Listing Multiples Method:

To find LCM by listing multiples method we will list down the multiples of given numbers.

Multiples of 21:

21426384105126147168189210

Multiples of 63:

63126189252315378441504567630

The lowest common multiple in the above lists will be the LCM of the given numbers.

63 is the lowest multiple which is common in the above lists.

∴ LCM(21, 63) = 63

If the HCF of two numbers is 21 and their product is 1323, what is their LCM?

If the LCM of two numbers is 63 and their product is 1323, what is their HCF?

HCF and LCM of two numbers is 21 and 63 respectively. If one number is 21, what is the other number?

Let other number be x.
Given:
HCF(21, x) = 21
LCM(21, x) = 63
∵ HCF × LCM = product of numbers
∴ 21 × 63 = 21 × x
∴ 1323 = 21x
∴ 1323⁄21 = x
∴ x = 63
Hence, the other number is 63.