This page offers a step-by-step solution to the specific question **NCERT Class 10th Mathematics - Real Numbers | find the lcm and hcf of the following pairs of int Answer ** from NCERT Class 10th Mathematics, Chapter Real Numbers.

Question 2

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Answer

**(i) 26 and 91**

First we have to find the L.C.M and H.C.F of 26, 91 using fundamental theorem of arithmetic,

26 = 13 × 2

91 = 13 × 7

For L.C.M - list all the prime factors (only once) of 26, 91 with their greatest power.

L.C.M (26, 91) = 13 × 2 × 7 = 182

For H.C.F – write all the common factors (only once) with their smallest exponent.

H.C.F (26, 91) = 13

Verification : L.C.M (26, 91) × H.C.F (26, 91) = 26 × 91

182 × 13 = 2366, => 2366 = 2366

Hence, proved.

**(ii) 510 and 92**

First we have to find the L.C.M and H.C.F of 510, 92 using fundamental theorem of arithmetic,

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

For L.C.M - list all the prime factors (only once) of 510, 92 with their greatest power.

L.C.M (510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460

For H.C.F – write all the common factors (only once) with their smallest exponent.

H.C.F (510, 92) = 2

Verification : L.C.M (510, 92) × H.C.F (510, 92) = 510 × 92

23460 × 2 = 46920, => 46920 = 46920

Hence, proved.

**(iii) 336 and 54**

First we have to find the L.C.M and H.C.F of 336, 54 using fundamental theorem of arithmetic,

336 = 2 × 2 × 2 × 2 × 3 × 7 = 2^{4} × 3 × 7

54 = 2 × 3 × 3 × 3 = 2 × 3^{3}

For L.C.M - list all the prime factors (only once) of 336, 54 with their greatest power.

L.C.M (336, 54) = 3024

For H.C.F – write all the common factors (only once) with their smallest exponent.

H.C.F (336, 54) = 2 × 3 = 6

Verification : L.C.M (336, 54) × H.C.F (336, 54) = 336 × 54

3024 × 6 = 18144 => 18144 = 18144

Hence, proved.

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