Page 65 - ICSE Math 6

The smallest common multiple of 10 and 3 is 30.

∴ LCM of 10 and 3 is 30.
As all the multiples of a number are divisible by the number itself, therefore LCM of the given numbers
is the smallest number which is exactly divisible by each of the given numbers. We can find the LCM
of the given numbers using the following methods:
(a) Common Multiple Method Maths Info

(b) Prime Factorization Method
The LCM of prime numbers is
(c) Division Method equal to their product.

Common multiple method

Step 1: Find some multiples of the given numbers.
Step 2: From the multiples obtained, select the multiples common to all the given numbers.
Step 3: Out of the common multiples, the smallest multiple is the LCM of the given numbers.

Example 28: Find the LCM of 4, 5 and 20 using the common multiple method.

Solution: Multiples of 4 are 4, 8, 12, 16, 20, 24, …
Multiples of 5 are 5, 10, 15, 20, 25, …

Multiples of 20 are 20, 40, 60, 80, 100, …
Common multiples are 20, 40, 60, …
∴ LCM of 4, 5 and 20 is 20.

Prime factorization method
Step 1: Find all the prime factors of all the given numbers.

Step 2: Identify the highest number of times each prime factor appears in any of the factorizations.
Step 3: The product of the prime factors with the highest power is the LCM of the given numbers.

Example 29: Find the LCM of 16, 96 and 448 using the prime factorization method.
Solution: Since, 16 = 2 × 2 × 2 × 2 = 2 4

5
96 = 2 × 2 × 2 × 2 × 2 × 3 = 2 × 3
6
448 = 2 × 2 × 2 × 2 × 2 × 2 × 7 = 2 × 7
The maximum number of times prime factor 2 occurs is 6 and prime factors 3 and 7
occur only once.

6
∴ LCM = 2 × 3 × 7 = 64 × 3 × 7 = 1,344
Division method

Step 1: Write the given numbers in a row separated by commas.
Step 2: Divide the numbers by a prime number which is a factor of at least two of the numbers.
Step 3: Write the quotients below the respective numbers and the numbers which are not divisible
as it is.
Step 4: Repeat steps 2 and 3 till no two numbers have a common factor.

Step 5: The product of all the divisors and the remaining quotients is the required LCM.

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