8. Find the least number which when divided by 30, 36, 54 and 63 leaves 8
as remainder in each case.
Answers
Given:
When the least number is divided by 30, 36, 54 and 63 leaves 8
as the remainder in each case.
To find:
The least number
Solution:
(1). We will first find the L.C.M. of 30, 36, 54 & 63 by using the prime factorisation method
Factors:
30 = 2 × 3 × 5
36 = 2 × 2 × 3 × 3
54 = 2 × 3 × 3 × 3
63 = 3 × 3 × 7
L.C.M:
∴ L.C.M. of 30, 36, 54 & 63 = 2 × 2 × 3 × 3 × 3 × 5 × 7 = 3780
(2). Now, we will add the remainder 8 to the L.C.M.
∴ Least Number = 3780 + 8 = 3788
Thus, the least number which when divided by 30, 36, 54 and 63 leaves a remainder 8 in each case is 3788.
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