how many times is the H.C.F of 64 and 124 contained in their L.C.M
HCF(64,124) = HCF(4*16,4*31) = 4
LCM(64,124) = 64*124 / HCF(64,124)
HCF 4
LCM 1984
To find the number of times the Highest Common Factor (HCF) of two numbers is contained in their Lowest Common Multiple (LCM), we need to divide the LCM by the HCF.
Given that the HCF of 64 and 124 is 4, we need to find how many times 4 is contained in their LCM.
The LCM of 64 and 124 can be found by multiplying the numbers and dividing by their HCF:
LCM = (64 x 124) / 4 = 1984
Now, we can find how many times 4 is contained in 1984:
1984 ÷ 4 = 496
Therefore, the HCF of 64 and 124 is contained 496 times in their LCM.
To find the number of times the Highest Common Factor (H.C.F) of two numbers is contained in their Lowest Common Multiple (L.C.M), we can use the following formula:
Number of times H.C.F is contained in L.C.M = L.C.M / H.C.F
In this case, the given numbers are 64 and 124.
Step 1: Determine the L.C.M of 64 and 124.
To find the L.C.M, we need to prime factorize both numbers.
Prime factorization of 64:
64 = 2 * 2 * 2 * 2 * 2 * 2 = 2^6
Prime factorization of 124:
124 = 2 * 2 * 31 = 2^2 * 31
To find the L.C.M, we take the highest power of each prime factor:
L.C.M = 2^6 * 31 = 1984
Step 2: Determine the H.C.F of 64 and 124.
To find the H.C.F, we need to find the common factors of both numbers.
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 124: 1, 2, 4, 31, 62, 124
Common factors: 1, 2, 4
The highest common factor is 4.
Step 3: Calculate the number of times H.C.F is contained in L.C.M.
Number of times H.C.F is contained in L.C.M = L.C.M / H.C.F
Number of times H.C.F is contained in L.C.M = 1984 / 4 = 496
Therefore, the H.C.F of 64 and 124 is contained 496 times in their L.C.M.