LCM and HCF

Lowest Common Factor and Highest Common Factor 

In this post, we will learn  Lowest Common Factor(LCM) and Highest Common Factor (HCF).

Factor and Multiples: If number 'a' divide number 'b' exactly then 'a' is a factor of 'b' and 'b' is multiple of 'a'.   

Prime Factorisation: It is possible to write any number natural number as a product of prime number and this product is unique for every number Example:

• 10: 2 x 5
• 11: 11
• 100: 2 x 2 x 5 x 5

Lowest Common Factor(LCM)

Prime Factorisation Method

Find L.C.M of 12, 16 and 30

Step 1: Resolve each number into its prime factor

• 12: 2 x 2 x 3
• 16: 2 x 2 x 2 x 2
• 30: 2 x 3 x 5

Step 2: Find highest power of the factor for each prime

• 2 x 2 x 3 = 2² x 3¹
• 2 x 2 x 2 x 2 = 2⁴
• 2 x 3 x 5 = 2¹ x 3¹ x 5¹

Step 3: L.C.M will be Product of highest power

LCM of 12, 16 and 30 = 2⁴ x 3¹ x 5¹ = 240 because 2, 3, 5 is unique prime (step 1) and highest power is 4, 1, 1 (step 2)

Highest Common Factor(HCF) 

Prime Factorisation Method

Find H.C.F of 144, 108 and 180

Step 1: Resolve each number into its prime factor

• 144: 2 x 2 x 2 x 2 x 3 x 3
• 108: 2 x 2 x 3 x 3 x 3
• 180: 2 x 2 x 3 x 3 x 5 

Step 2: Find common factor 

• 144: 2 x 2 x 2 x 2 x 3 x 3
• 108: 2 x 2 x 3 x 3 x 3
• 180: 2 x 2 x 3 x 3 x 5 

Step 3: HCF will be product of common factor

HCF of 144, 108 and 180 will be 2 x 2 x 3 x 3 = 36

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