Page 70 - ICSE Math 5

4. Find the L.C.M. of the following numbers by common division method.
(a) 25 and 100 (b) 48, 64 and 60 (c) 18, 27 and 63

Relationship between H.C.F. and L.C.M. of Two Numbers

Let’s consider an example to learn about the relationship between H.C.F. and L.C.M. of two
numbers.

Consider two numbers, say 9 and 15, and find their L.C.M. and H.C.F.
H.C.F. of 9 and 15 is 3.

L.C.M. of 9 and 15 is 45.
 Product of H.C.F. and L.C.M. of two numbers = 3 × 45 = 135.

Also, the product of the two given numbers = 9 × 15 = 135.
So, we can say that the product of H.C.F. and L.C.M. of two numbers is equal to the product of
the given two numbers, i.e.,

H.C.F. × L.C.M. = First number × Second number

We can also say that;

First number × Second number
• H.C.F. =
L.C.M. of two numbers Mental Maths
First number × Second number Find the H.C.F. and L.C.M. of
• L.C.M. = 7 and 13.
H.C.F. of two numbers

H.C.F. × L.C.M.
• First number =
Second number

H.C.F. × L.C.M.
• Second number =
First number
Example 19: The H.C.F. and L.C.M. of two numbers are 6 and 120 respectively. If the first number
is 24, find the second number.

Solution: H.C.F. of two numbers = 6
L.C.M. of two numbers = 120

First number = 24
H.C.F. × L.C.M. 6 × 120
 Second number = = = 30
First number 24
So, the second number is 30.

Example 20: The L.C.M. of 12 and 18 is 36. Find their H.C.F.
First number × Second number
Solution: H.C.F. =
L.C.M.
6
12 × 18
=
36
2
So, the H.C.F. of 12 and 18 is 6.

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