Question
The sum and the difference of the
L.C.M and H.C.F of two numbers are 486 and 342. If one of the numbers is 18, find the other number.
Solution
ATQ,
Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively
Then, (a + b) = 486
And (a - b) = 342
So, (a + b) + (a - b) = 486 + 342 = 828
Or, a = 828 ÷ 2 = 414
So, b = 486 - 414 = 72
The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (414 × 72) ÷ 18 = 1656
More HCF and LCM Questions
- Calculate the number of factors of 480.
- The HCF of two numbers is 20. If their product is 16000, then how many such pairs exist?
- What is the difference between the LCM and HCF of 21, 49?
- Find the largest number of the five digit which is exactly divisible by 48, 72 and 108.
- Find the smallest 4-digit number that is exactly divisible by 14, 20 and 27.
- The HCF of two numbers is 12 and their LCM is 180. If one of the numbers is 36, find the other number.
- The greatest number, which when subtracted from 6254, gives a number exactly divisible by each of 20, 25, 30 and 35, is:
- The H.C.F of two numbers is 2 and their L.C.M is 117. If one of the numbers is 13, find the other?
- The square of sum of two numbers is 36,864 and the sum of squares of the same two numbers is 21,024. If their H.C.F. is 12, then find their L.C.M.
- If the product of two numbers is 3026 and their LCM is 89 then their HCF is:
Relevant for Exams:
