Question

Use Euclid's division algorithm to find HCF of $420$ and $130$, hence find LCM.

Answer 1

Two numbers are given as $420$ and $130$

Apply Euclid's Division Lemma on $420$ and $130$

$420=130\times 3+30$

As $r\ne 0$, so again apply Euclid's division Lemma on $130$ and $30$

$130=30\times 4+10$

As $r\ne 0$, so again apply Euclid's division Lemma on $30$ and $10$

$30=10\times 3+0$

As $r=0$, so HCF $=10$

Therefore, HCF of $420$ and $130$ is $10$.

We know that, if $a,b$ are two numbers then

$a\times b$ $=$ LCM $(a,b)$ $\times$ HCF $(a,b)$

$\Rightarrow$ $420\times 130$ $=$ LCM$(a,b)$ $\times$ $10$

$\Rightarrow$ $\frac{420\times 130}{10}=$ LCM$(a,b)$

$\Rightarrow$ $5460=$ LCM $(a,b)$

Therefore, LCM$(130,420)=5460$