# The HCF of 1236, 2568 and a third number ‘x’ is 12. If their LCM is 2

| The HCF of 1236, 2568 and a third number ‘x’ is 12. If their LCM is 2

^{3}× 3^{2}× 5^{1}× 103 × 107, then the number ‘x’ is:A. 2^{2} × 3^{2} × 7^{1}

B. 2^{2} × 3^{3} × 10^{3}

C. 2^{2} × 3^{2} × 5^{1}

D. None of these

### Right Answer is: C

#### SOLUTION

HCF of 1236, 2568 and a third number ‘x’ is 12

1236 = 12 × 103

2568 = 2 × 12 × 107

HCF of 1236 & 2568 = 12

LCM of 1236 and 2568 = 2 × 12 × 103 × 107

When we include third number x, LCM of these three number will become = 2^{3} × 3^{2} × 5^{1} × 103 × 107

So, the third No. will include ‘5^{1’} term in it along with the HCF 12.

So the third No. will be = 2^{3} × 3^{2} × 5^{1}

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