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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

relationsHiP Between HcF and lcM

Consider any two numbers say 18 and 24. Let us find their HCF and LCM.

HCF of 18 and 24 LCM of 18 and 24

18 24 1 2 18, 24
– 18 2 9, 12
6
2 9,
6 18 3 3 9, 3
– 18 3 3, 1

0 1, 1
So, HCF of 18 and 24 = 6 and LCM of 18 and 24 = 2 × 2 × 2 × 3 × 3 = 72.
Product of HCF × LCM = 6 × 72 = 432.
Now, product of the given two numbers = 18 × 24 = 432.

What do you observe? Clearly, product of HCF and LCM of two numbers = product of the
numbers.

HCF × LCM = 1 number × 2 number
st
nd
This relationship between the HCF and LCM is useful for solving many problems.

example 1: The HCF and LCM of two numbers are 15 and 180 respectively. If one of the
numbers is 45, find the other number.

Solution: Given that: HCF = 15, LCM = 180 and one number = 45
We know that, HCF × LCM = 1 number × 2 number.
nd
st
nd
15 × 180 = 45 × 2 number
nd
2700 = 45 × 2 number
2 number = 2700 = 60
nd
45
Thus, the other number is 60.

example 2: The LCM of 165 and 275 is 825. Find their HCF.
Solution: Given, two numbers are 165 and 275 and their LCM = 825.

We know that, HCF × LCM = 1 number × 2 number.
st
nd
HCF × 825 = 165 × 275
HCF × 825 = 45375

HCF = 45375 = 55
825
Thus, the HCF of 165 and 275 is 55.

teacher’s Explain to the students that the HCF of two co-prime numbers is 1 and the LCM of two co-prime numbers is
tip the product of those numbers. Explain that if a number is a factor of another number, then their HCF is the
smaller number and their LCM is the greater number.

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