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