LCM BY PRIME FACTORISATION METHOD
The LCM of the given numbers can be found using
the prime factorization method by first finding the prime factorization of each
number, then identifying the highest power of each prime factor, and finally
multiplying the prime factors with their highest powers.
Steps for finding LCM by prime factorisation method
Step 1: Write the prime factorisation of each number.
Step 2: For each prime factor, determine the highest
power that appears in any of the factorizations.
Step 3: Multiply the prime factors
raised to their highest powers together.
EXAMPLE:
1. Find the LCM of 24 and 36.
Step 1:
Prime factorization of 24= 2 x 2 x 2 x 3 = 2³ x 3
Prime factorization of 36: 2 x 2 x 3 x 3 = 2² x 3²
Step 2:
Identify Highest Powers:
Prime Factor: 2
Highest power is 2³
Prime Factor: 3
Highest power is 3²
Step 3:
LCM = 2³ x 3²
= 8 x 9
= 72
LCM of 24 and 36 = 72.
2. Find the LCM of 12, 18, and
20.
Step 1:
Prime factorization of 12= 2 x 2 x 3 = 2² x 3
Prime factorization of 18= 2 x 3 x 3 = 2 x 3²
Prime factorization of 20= 2 x 2 x 5 = 2² x 5
Step 2:
Identify Highest Powers:
Prime Factor: 2
Highest power is 2²
Prime Factor: 3
Highest power is 3²
Prime Factor: 5
Highest power is 5
Step 3:
LCM = 2² x 3² x 5
= 4 x 9 x 5
= 180
LCM of 12, 18, and 20 = 18
Worksheet pdf given below
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