Question

Dev has some marbles. if he makes groups of 3 each, he is left with 1 marble. if he makes groups of 5 each, he is again left with 1 marble and if he makes groups of 7 each, he is again left with 1 marble. how many marbles does he have

Answer 1

take the lcm of 3,5 and 7.

we will get 105.

add 1 to 105=106

Dev has 106 marbles.

Answer 2

• The least marbles dev does have equal to 106 .

Given :- If dev makes groups of 3 each, he is left with 1 marble. if he makes groups of 5 each, he is again left with 1 marble and if he makes groups of 7 each, he is again left with 1 marble.

To Find :- The least possible value of marbles he have ?

Concept used :-

• The least number which when divided by a, b and c leaves the same remainder ‘r’ each case is equal to :- LCM(a, b, c) + r

Solution :-

according to given data we have,

→ Group of 3 marble each = 1 marble left alone .

→ Group of 5 marble each = 1 marble left alone .

→ Group of 7 marble each = 1 marble left alone .

conclusion :- we need to find the least value of marbles which one divided by 3, 5 and 7 leaves same remainder 1 in each case .

So,

→ Required number of marbles = LCM(3, 5, 7) + 1

finding LCM of 3, 5 and 7 by prime factorisation method :-

→ 3 = 1 × 3

→ 5 = 1 × 5

→ 7 = 1 × 7

then,

→ LCM = 1 × 3 × 5 × 7 = 105

therefore,

→ Required number of marbles = 105 + 1 = 106 (Ans.)

Hence, the least marbles dev does have equal to 106 .

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