How many times of HCF of 64 and 126 contained in their LCM?
To find out how many times the highest common factor (HCF) of two numbers is contained in their lowest common multiple (LCM), we can use the following formula:
LCM(a, b) = (a * b) / HCF(a, b)
Given that the HCF of 64 and 126 is 2, we can substitute this value into the formula:
LCM(64, 126) = (64 * 126) / 2
LCM(64, 126) = 8064 / 2
LCM(64, 126) = 4032
Therefore, the HCF of 64 and 126 is contained in their LCM 4032/2 = <<4032/2=2016>>2016 times.
To find out how many times the highest common factor (HCF) of two numbers is contained in their least common multiple (LCM), you can follow these steps:
Step 1: Find the HCF of the given numbers, 64 and 126.
To find the HCF, you can use the Euclidean algorithm or prime factorization method. In this case, the prime factorization method is faster:
Prime factorization of 64: 2^6
Prime factorization of 126: 2 * 3^2 * 7
Step 2: Identify the common prime factors of the two numbers and their lowest powers. In this case, the only common prime factor is 2, with the lowest power being 2^1.
Step 3: Calculate the LCM of the two numbers.
LCM of 64 and 126 = (2^6) * (3^2) * 7 = 2016
Step 4: Divide the LCM by the HCF to find out how many times the HCF is contained.
Number of times HCF is contained in LCM = LCM / HCF
Number of times HCF is contained in 2016 = 2016 / 2^1 = 1008
Therefore, the HCF of 64 and 126 is contained 1008 times in their LCM.