What is the product of LCM and HCF of the following numbers 12,9, and 15.
First, we need to find the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the given numbers.
Prime factorizing the given numbers:
12 = 2 × 2 × 3
9 = 3 × 3
15 = 3 × 5
HCF is the product of the common prime factors raised to their lowest power, which is 3 in this case.
LCM is the product of all prime factors, each raised to their highest power. In this case, we have:
2 × 2 × 3 × 3 × 5 = 180
Therefore, the product of LCM and HCF is:
180 × 3 = 540.
Hence, the product of LCM and HCF of the given numbers 12, 9, and 15 is 540.