Four bells toll at an interval of 8, 12, 15 and 18 seconds respectively. All the four begin to toll together. Find the number of times they toll together in one hour excluding the one at the start.

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Solution

Q.
Four bells toll at an interval of 8, 12, 15 and 18 seconds respectively. All the four begin to toll together. Find the number of times they toll together in one hour excluding the one at the start.

Ans.
(10)

Prime factorisation of the given numbers are:

$8 = 2 \times 2 \times 2 = 2^{3}$

$12 = 2 \times 2 \times 3 = 2^{2} \times 3^{1}$

$15 = 3 \times 5 = 3^{1} \times 5^{1}$

$18 = 2 \times 3 \times 3 = 2^{1} \times 3^{2}$

$LCM (8, 12, 15 and 18) = 2^{3} \times 3^{2} \times 5^{1} = 8 \times 9 \times 5 = 360 sec = 6 min$

$∴$ Four bells toll together in one hour $= 60 \div 6 = 10$ times.

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