CUET CUET General Test 2024 - The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is: | PYQs + Solutions

CUET General Test 2024

Number System

HCF & LCM

Medium

The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is:

160

164

168

172

Correct Option: 3

Let the HCF be

h

. Then the LCM is

60h

According to the problem, we have:

h + 60h = 854

This simplifies to:

61h = 854

Thus,

h = \frac{854}{61} = 14

Now, the LCM is:

LCM = 60h = 60 \times 14 = 840

Using the relationship between LCM, HCF, and the two numbers, we have:

LCM = \frac{a \times b}{HCF}

where

a = 70

and

b

is the unknown number.

Substituting the known values:

840 = \frac{70 \times b}{14}

This simplifies to:

840 = 5b

Thus,

b = \frac{840}{5} = 168

The other number is 168.