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\\February 16, 2024 2:20 PM Surender Prajapati Proof 5 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 given two numbers = 18 × 24 = 432.
What do you observe? Clearly, product of HCF and LCM of two numbers = product of their

numbers.
st
nd
Thus, HCF × LCM = 1 number × 2 number
This relationship between HCM 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
st
nd
We know that, HCF × LCM = 1 number × 2 number.
nd
Here, 15 × 180 = 45 × 2 number
nd
2700 = 45 × 2 number
So, 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.

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

HCF = 45375 = 55
825
Thus, the HCF of 165 and 275 is 55.
teacher’s
tip Explain to the children that HCF of two co-prime number is 1 and LCM of two co-prime numbers is the product
of that numbers. And if a number is factor of another number, then their HCF is the smaller number and LCM
is the greatest number.

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