Question

The hcf of two numbers in the ratio 2: 7 is 23. find their lcm

Answer 1

According to the question, ratio of two numbers is ( 2:7)

Let consider the numbers are 2x and 7x          ( given)

∴ HCF of 2x and 7x  will be =x

(and  HCF of 2 and 7  will be = 1)

According the question HCF of two numbers is 23.     ( given)

∴ x = 23

Now putting the value of  'x' we will get:-

2x = 2 × 23 = 46   ..       ( 1 )

7x = 7 × 23= 161   ..        ( 2 )

∴ Equation (1)  × equation ( 2) =LCM × HCF

LCM = [ ( 1 ) × ( 2 )] ÷ HCF

LCM = ( 46 × 161 ) ÷ 23

LCM = $\frac{7406}{23}$

LCM = $322$

Hence LCM of two numbers is 322.

Ans :-  LCM of two numbers is 322.

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