Question 37

The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54. is

Solution

The given numbers can be expanded as follows

$$24=2^{3} \times 3$$

$$32=2^{5}$$

$$36=2^{2} \times 3^{2}$$

$$54=2 \times 3^{3}$$

The L.C.M of the above numbers=$$2^{5} \times 3^{3}=864$$

Thus, the lowest number when added by 5 is divisible by the given numbers=864-5=859

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