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

Question

Verified by Toppr

Answer 1

1) $26 = 2 \times 13$ and $91 = 1 \times 91$
$HCF = 1$ and $LCM = 2 \times 13 \times 91 = 2366$
verification: $1 \times 2366 = 26 \times 91 \Rightarrow 2366 = 2366$

2) $510 = 2 \times 3 \times 5 \times 17$ and $92 = 2^{2} \times 23$
$HCF = 2$ and $LCM = 2^{2} \times 3 \times 5 \times 17 \times 23 = 23460$
verification: $2 \times 23460 = 92 \times 510 \Rightarrow 46920 = 46920$

3) $54 = 2 \times 3^{3}$ and $336 = 2^{4} \times 3 \times 7$
$HCF = 6$ and $LCM = 2^{4} \times 3^{3} \times 7 = 3024$
verification: $6 \times 3024 = 336 \times 54 \Rightarrow 18144 = 18144$

Answer 2

1)

26 = 2 \times 13

and

91 = 1 \times 91

HCF = 1

and

LCM = 2 \times 13 \times 91 = 2366

verification:

1 \times 2366 = 26 \times 91 \Rightarrow 2366 = 2366

2)

510 = 2 \times 3 \times 5 \times 17

and

92 = 2^{2} \times 23

HCF = 2

and

LCM = 2^{2} \times 3 \times 5 \times 17 \times 23 = 23460

verification:

2 \times 23460 = 92 \times 510 \Rightarrow 46920 = 46920

3)

54 = 2 \times 3^{3}

and

336 = 2^{4} \times 3 \times 7

HCF = 6

and

LCM = 2^{4} \times 3^{3} \times 7 = 3024

verification:

6 \times 3024 = 336 \times 54 \Rightarrow 18144 = 18144