Skip to main contentSkip to solution

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:

Solution

Correct Option: 3

Let the HCF be hh. Then the LCM is 60h60h.

According to the problem, we have:

h+60h=854h + 60h = 854

This simplifies to:

61h=85461h = 854

Thus,

h=85461=14h = \frac{854}{61} = 14.

Now, the LCM is:

LCM=60h=60×14=840LCM = 60h = 60 \times 14 = 840.

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

LCM=a×bHCFLCM = \frac{a \times b}{HCF},

where a=70a = 70 and bb is the unknown number.

Substituting the known values:

840=70×b14840 = \frac{70 \times b}{14}.

This simplifies to:

840=5b840 = 5b.

Thus,

b=8405=168b = \frac{840}{5} = 168.

The other number is 168.

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question