Question

The LCM of two coprime numbers is 1,302. If one
of the numbers is 42, what is the other number? in detail​

Answer 1

AnswEr:

$\large\bold{\underline{\sf{\blue{\:\:Given\:\:}}}}$

• LCM of Numbers is 1,302 & one number is 42.

Let us Consider that the other Number be x.

We know that,

Both Numbers are Co primes.

Co Primes have only 1 as their Factor.

So, HCF would be 1.

$\longrightarrow\sf\: HCF \: = \: 1$

$\longrightarrow{\underline{\boxed{\sf{\red{LCM \: \times\; HCF\: =\: Product\: of \: two \; Numbers}}}}}$

$\diamond\small\bold{\underline{\sf{\blue{Finding\: other\: Number}}}}$

$\longrightarrow\sf\: 1 \times \: 1302 \: = \: 42 \times\: x$

$\longrightarrow\sf\: 1302 = 42x$

$\longrightarrow\sf\:x = \dfrac{1302}{42}$

$\longrightarrow\large{\underline{\boxed{\sf{\red{x \: =\: 31}}}}}$

$\small{\underline{\sf{\blue{Hence,\:The\; Other\; Number\; is\; 31.}}}}$

$\rule{200}2$

Answer 2

$\bf{\underline{\underline{Given\: :}}}$

$\mathsf{\bigstar\: LCM\:of\:two\:coprime\:no's = 1,302}$

$\mathsf{\bigstar\: One\:number = 42}$

$\bf{\underline{\underline{To\:find\: :}}}$

$\mathsf{\bigstar\: Other\:number}$

$\bf{\underline{\underline{Solution\: :}}}$

$\mathsf{Let\:one\:number = a = 42}$

$\mathsf{and\:other\:number = b}$

$\mathsf{We\:know\:that}$

$\mathsf{HCF \:of\:coprime\:no's = 1}$

$\mathtt{HCF(a,b) × LCM(a,b) = Product \:of\: a\: and\: b}$

$\mathtt{\rightarrow\: 1 × 1302 = a × b}$

$\mathtt{\rightarrow\: 1 × 1302 = 42 × b}$

$\mathtt{\rightarrow\: b = \Large{\frac{1302}{42}}}$

$\fbox{\Large{\mathtt{\green{\rightarrow\: b = 31}}}}$

$\text{Therefore, the other number = 31}$