Question: Two fountains in a park spray water at intervals of 25 seconds and 40 seconds respectively. If they spray together at 10:00 AM, after how many seconds will they spray together again?
(A) 100 seconds
(B) 200 seconds
(C) 400 seconds
(D) 600 seconds
Solution:
We need to find the LCM of 25 and 40.
Prime factorization of 25:
25 = 5²
Prime factorization of 40:
40 = 2³ × 5
LCM is the product of the highest powers of all prime factors:
LCM (25,40) = 2³ × 5² = 8×25 = 200
So, the fountains will spray together again after 200 seconds.
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