Question

Three numbers are in the ratio 3 : 5 : 7 and their LCM is 2520. Their HCF is (a) 24 (b) 12 (c) 8 (d) 16 ​

Answer 1

Answer:

Given :-

• Three numbers are in the ratio of 3 : 5 : 7 and their LCM is 2520.

To Find :-

• What is the HCF of the three numbers.

Solution :-

Let,

➸ First Number = 3x

➸ Second Number = 5x

➸ Third Number = 7x

So, their LCM is 105x

According to the question :

➳ 105x = 2520

➳ x = 2520/105

➳ x = 24/1

➳ x = 24

Hence, the numbers are :

★ First Number :

➟ First Number = 3x

➟ First Number = 3(24)

➟ First Number = 72

★ Second Number :

➟ Second Number = 5x

➟ Second Number = 5(24)

➟ Second Number = 120

★ Third Number :

➟ Third Number = 7x

➟ Third Number = 7(24)

➟ Third Number = 168

$\therefore$ The HCF is 24 .

Hence, the correct options is option no (a) 24 .