If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is
203400
194400
198400
205400
Let the HCF be x and the LCM of the two numbers be y.
It is given that the sum of the HCF and LCM is 1260
x + y = 1260 …… (i)
And, LCM is 900 more than HCF.
y = x + 900 …… (ii)
Substituting (ii) in (i), we get:
`x + x + 900 = 1200`
`2x +900=1260`
`2x = 1260 -900`
`2x = 360`
x = 180
Substituting x = 180 in (ii), we get:
y = 180 + 900
y = 1080
We also know that the product the two numbers is equal to the product of their LCM and HCF
Thus the product of the numbers
= 194400(180)
= 194400
Hence, the correct choice is (b).
Concept: Euclid’s Division Lemma
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10 Questions 10 Marks 10 Mins
Given:
The ratio of two numbers = 5 ∶ 9
LCM = 765
Concept Used:
The product of two numbers = LCM × HCF
Calculation:
Let the two numbers be 5x and 9x
According to the question, we have
The LCM of 5x and 9x = 5 × 9 × x
⇒ 45x
Now, the LCM of two numbers is
45x = 765
⇒ x = 765/45
⇒ x = 17
The first number = 5x
⇒ 5 × 17
⇒ 85
The second number = 9x
⇒ 9 × 17
⇒ 153
∴ The two numbers are 85 and 153.
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