Math, asked by BrainlyHelper, 1 year ago

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of the integers:
(i)26 and 91
(ii)510 and 92
(iii)336 and 54

Answers

Answered by nikitasingh79
223

SOLUTION :  

(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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kritisanon28: hi
Answered by Anonymous
139
Solutions :-

Q: Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of the integers :-

(i) 26 and 91

The prime factor of 26 and 91 :-

26 = 2 x 13
91= 7 x 13

LCM of 26 and 91 = 2 x 7 x 13 = 182
HCF of 26 and 91 = 13

Verification :-
LCM x HCF = 26 x 91 = 2366
Product of integers = 182 x 13 = 2366

LCM x HCF = product of the integers. Hence, verified

(ii) 510 and 92

The prime factor of 510 and 92 :-

510 = 2 x 3 x 5 x 17
92 = 2 x 2 x 23

LCM of 510 and 92 = 2 x 2 x 3 x 5 x 17 x 23 = 23460
HCF of 510 and 92 = 2

Verification :-
LCM x HCF = 510 x 92 = 46920
Product of integers = 23460 x 2 = 46920

LCM x HCF = product of the integers. Hence, verified


(iii) 336 and 54

The prime factor of 336 and 54 :-

336 = 2 x 2 x 2 x 2 x 3 x 7
54 = 2 x 3 x 3 x 3

LCM of 336 and 54 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 = 3024
HCF of 336 and 54 = 6

Verification :-
LCM x HCF = 336 x 54 = 18144
Product of integers = 3024 x 6 = 18144
LCM x HCF = product of the integers. Hence, verified
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