Question

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

1. $26$ and $91$
2. $510$ $$and $92$
3. $336$ and $54$

Answer 1

(i) $26$ and $91$
$26=2×13$
$91=7×13$
HCF $= 13$
LCM$=2×7×13=182$
Product $×$of the two numbers $= 26×91=2366$
HCF$×$LCM$=13×182=2366$

Hence, product of two numbers = HCF $×$ LCM

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(ii) $510$ and $92$
$510=2×3×5×17$
$92=2×2×23$
HCF $= 2$
LCM$=2×2×3×5×17×23=23460$
Product of the two numbers $= 510×92=46920$
HCF$×$LCM$=2×23460$
$= 46920$

Hence, product of two numbers = HCF $×$ LCM

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(iii) $336$ and $54$
$336=2×2×2×2×3×7$
$336=2^4×3×7$
$54=2×3×3×3$
$54=2×3^3$
HCF$=2×3=6$
LCM$=2^4×3^3×7=3024$
Product of the two numbers $= 336×54=18144$
HCF$×$LCM$=6×3024=18144$

Hence, product of two numbers = HCF $×$ LCM