Let us consider some of the word problems on l.c.m. (least common multiple).
1. Find the lowest number which is exactly divisible by 18 and 24.
We find the L.C.M. of 18 and 24 to get the required number.
L.C.M. = 2 × 3 × 3 × 4 = 72
Therefore, 72 is the required number.
2. Find the lowest number which is less by 5 to be divided by 16, 24 and 36 exactly.
We find the L.C.M. of 16, 24 and 36.
L.C.M. = 2 × 2 × 2 × 3 × 2 × 3 = 144
Now subtract 5 from 144 to get the required number.
144  5 = 139
Therefore, 139 is the required number.
3. Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly.
We find the L.C.M. of 25, 40 and 60.
L.C.M. = 2 × 2 × 5 × 5 × 2 × 3 = 600
Therefore, the required number is 600 + 6 = 606.
4. Find the lowest number which leaves 3 as remainder when divided by 8, 12 and 16.
We find the L.C.M. of 8, 12 and 16.
L.C.M. = 2 × 2 × 2 × 3 × 2 = 48
If we add 3 to 48 it becomes 51 which leaves 3 as remainder when divided by 8, 12 and 16.
Therefore, the required number is 48 + 3 = 51.
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