Question

if h•cf (26, 169)= 13 then L•cm (26,169=__________​

Answer 1

$\large\underline{\sf{Given- }}$

• First number = 26

• Second number = 169

• HCF (26, 169) = 143

$\large\underline{\sf{To\:Find - }}$

• LCM (26, 169)

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}$

Let a and b are two positive integers having HCF(a, b) and LCM(a, b), then

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

$\large\underline{\sf{Solution-}}$

Given that

• First number, a = 26

• Second number, b = 169

• HCF (26, 169) = 13

Using property,

$\rm :\longmapsto\:LCM(a, b) \times HCF(a, b) = a \times b$

$\rm :\longmapsto\:LCM(26, 169) \times HCF(26, 169) = 26 \times 169$

$\rm :\longmapsto\:LCM(26, 169) \times 13 = 26 \times 169$

$\rm :\longmapsto\:LCM(26, 169) = 338$

Explore more :-

Some of the important properties of HCF and LCM are as under:

• The HCF of given numbers is never greater or more than any of the numbers.

• The LCM of given numbers is never less than any of the numbers.

• The HCF of two or more prime numbers is always 1.

• The LCM of two or more prime numbers is their product.

• The product of two numbers, a and b, is equal to the product of their HCF and LCM. It is also known as LCM and HCF formula discussed above.