## HCF and LCM questions

**Problem 1**: Least number which when divided by 35,45,55 and leaves remainder 18,28,38; is?

**Solution**:

i) In this case we will evaluate l.c.m.

ii) Here the difference between every divisor and remainder is same i.e. 17.

**Therefore,** required number = l.c.m. of (35,45,55)-17 = (3465-17)= 3448.

**Problem 2**: Least number which when divided by 5,6,7,8 and leaves remainder 3, but when divided by 9, leaves no remainder?

**Solution**:

l.c.m. of 5,6,7,8 = 840

Required number = 840 k + 3

Least value of k for which (840 k + 3) is divided by 9 is 2

**Therefore,** required number = 840*2 + 3

= 1683

**Problem 3**: Greater number of 4 digits which is divisible by each one of 12,18,21 and 28 is?

**Solution**:

l.c.m. of 12,18,21,28 = 254

Therefore, required number must be divisible by 254.

Greatest four digit number = 9999

On dividing 9999 by 252, remainder = 171

**Therefore,** 9999-171 = 9828.