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Question

Find the $$HCF$$ and $$LCM$$ of $$29029$$ and $$1740$$ by using the fundamental theorem of arithmetic.


Solution

HCF (29029, 1740)
$$ 29029 > 1740$$
$$29029 = 1740 \times 16 +1189$$
$$ 1740 = 1189 +551$$
$$ 1189 = 551 \times 2 +87$$
$$ 551 = 87 \times 6 + 29$$
$$87 = 29 \times 3 +0$$
$$\therefore H.C.F = 29$$
$$\therefore $$ Product of number = L.C.M $$\times $$ HCF
$$29029 \times 1740 = LCM \times 29$$
$$ 50510460 = LCM \times 29$$
$$LCM = 1741740$$

Maths

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