Math, asked by siaagrawal2503, 8 months ago

Find the LCM and HCF of the following pairs of numbers and verify that LCM x HCF = product of the two numbers. 26 and 91 510 and 92

Answers

Answered by Anonymous
4

Answer:

(i) Given :First number : 26

Second number : 91

The prime factors of 26 and 91 are :

26 = 2 x 13

91= 7 x 13

L.C.M (26,91) = 2 x 7 x 13

L.C.M of (26, 91) =182

[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]

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

[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]

We know that, L.C.M x H.C.F = First number x Second number

182 x 13 = 26 x 91

2366 = 2366

Hence verified

(ii) Given :First number : 510

Second number : 92

The prime factors of 510 and 92 are :

510 = 2 x 3 x 5 x 17

92 = 2 x 2 x 23 = 2² × 23

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

L.C.M (510 ,92) = 23460

[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]

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

[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]

We know that, L.C.M x H.C.F = First Number x Second Number

23460 x 2 = 510 x 92

46920 = 46920

Hence verified.

(iii) Given : First number : 336

Second number : 54

The prime factors of 336 and 54 are :

336 = 2 x 2 x 2 x 2 x 3 x 7 = 2⁴ × 3¹ × 7¹

54 = 2 x 3 x 3 x 3 = 2¹ × 3³

L.C.M (336 , 54) = 2⁴ × 3³× 7 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7

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

[LCM of two or more numbers = product of the greatest power of each prime factor involved in the numbers, with highest power.]

H.C.F (336 , 54) = 2 × 3

H.C.F (336 , 54) = 6

[HCF(Highest Common Factor) of two or more numbers = Product of the smallest Power of each common prime factor involved in the numbers.]

We know that, L.C.M x H.C.F = First Number x Second Number

3024 x 6 = 336 x 54

18144 = 18144

Hence verified

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