Page 89 - ICSE Math 4

Common Division Method or Prime Factorization Method

In this method, we fi nd the H.C.F. of two or more numbers by dividing them together

by the least common factor and then mul plying them to get the H.C.F. of the given
numbers.
Example 15: Find the H.C.F. of 15 and 30 using common division method.

Solu on: Step 1: Write the given numbers 15 and 30 in a row by 15, 30
separa ng them using commas as shown.

Step 2: Divide 15 and 30 by the smallest factor that
is common to both the numbers to fi nd their
quo ents. 3 15, 30

Here, both 15 and 30 are divisible by 3. So, 3 is the 5, 10
common factor. We get 5 and 10 as the quo ents of
15 and 30, respec vely.
Step 3: Divide the obtained quo ents by the smallest
3 15, 30
common factor. We know that 5 and 10 are divisible
5 5, 10
by 5, thus, 5 is the common factor. We get 1 and 2
1, 2
as the quo ents of 5 and 10, respec vely.

Since there are no common factors to divide 1 and 2 any more, we
will stop here.
Step 4: Write the common factors, i.e., 3 and 5 that are on the le column
and mul ply them to get the H.C.F. of 15 and 30.

So, the H.C.F. of 15 and 30 = 3 × 5 = 15.

Least Common Multiple (L.C.M.)

Least Common Mul ple (L.C.M.) is the smallest common mul ple of the given numbers.
Facts about L.C.M.

• The product of two prime numbers gives their L.C.M.
For example, 2 × 3 = 6 where 6 is the L.C.M. of 2 and 3.

3 × 5 = 15 where 15 is the L.C.M. of 3 and 5.
5 × 7 = 35 where 35 is the L.C.M. of 5 and 7.

• If the smaller number in the given numbers Mental Maths
is a factor of the greater number, then the
Find:
greater number will be the L.C.M. of the two
(a) the L.C.M. of 5 and 10 = ________
numbers.
(b) the L.C.M. of 6 and 18 = ________
For example, let’s fi nd the L.C.M. of 8 and 24. (c) the L.C.M. of 10 and 40 = ________
Mul ples of 8 are 8, 16, 24, 32, 40, ...

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