Question

find the LCM and HCF of 3 into 5 ^ 2 and 3 ^ 2 into 7 ^ 2

Answer 1

Given numbers :

3 × 5² and 3² × 7²

Prime factorisation –

3 × 5² = 3 × 5 × 5 × 1

3² × 7² = 3 × 3 × 7 × 7 × 1

Now,

HCF = Multiplication of Common terms

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HCF = 3 × 1 = 3

LCM = Multiplication of numbers have highest powers.

In the able prime Factorisation, we see that 3 has the highest power of 2 and 7 has the highest power of 2 and 5 also has 2.

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LCM = 3² × 5² × 7² = 9 × 25 × 49 = 11025