Question

Find the least number which when divided by 28, 32, 40 and 56 leaves a remainder of 11 in each case? 1131 1000 1100 1141

Answer 1

we need to find LCM of 28,32,40,56

Answer 2

Question :- Find the least number which when divided by 28, 32, 40 and 56 leaves a remainder of 11 in each case ? 1131 1000 1100 1141 ?

Solution :-

For Least Number first we will find LCM of Given Numbers .

Prime Factors of 28 ,32 ,40 ,56 :-

→ 28 = 2*2*7 = 2² * 7

→ 32 = 2 * 2 * 2 * 2 * 2 = 2⁵

→ 40 = 2*2*2 * 5 = 2³ * 5

→ 56 = 2 * 2 * 2 * 7 = 2³ * 5

LCM = 2⁵ * 7 * 5 = 32 * 35 = 1120 .

Therefore,

→ Least Number leaves a remainder of 11 in each case is = LCM of Number + 11

→ 1120 + 11

→ 1131 (Ans.)