Find the smallest square number which is divisible by each of the numbers 6, 9 and 15 ?
We will first find out the L.C.M of 6, 9 and 15.
L.C.M of 6, 9, 15 = 2 × 3 × 3 × 5 = 2 × 32 × 5 = 90
Since, we need to find the smallest square number divisible by 6, 9 and 15 and in above prime factorization of the numbers we observe that 2 and 5 does not appear in pair, therefore we multiply the L.C.M, 90 by 2 × 5.
Hence,
The required smallest square number = 90 × 2 × 5 = 900.