Let gcf(a, b) be the abbreviation for the greatest common factor of a and b, and let lcm(c, d) be the abbreviation for the least common multiple of c and d. what is gcf(lcm(8, 14), lcm(7,

Answer will be 28

Step-by-step explanation:

We have to find the GCF( LCM(8,14) , LCM (7,12) )

Here GCF is stands for greatest common factor and LCM is stands for lowest common factor

Let first find LCM of (8,14)

8 = 2×2×2

14 = 2×7

So LCM will be 2×2×2××7 = 56

Now LCM of (7,12)

7 = 7×1

12 = 2×2×3

So LCM will be 2×2×3×7 = 84

Now GCF of (56,84)

56 = 2×2×2×7

84=2×2×3×7

So GCF will be 2×2×7 = 28

Solution 1:

The least common multiple of 8=2^3 and 14=2*7 is 2^3*7 = 8*7 = 56. The least common multiple of 7 and 12 is 7*12=84. The greatest common factor of 56=2^3*7 and 84=2^2 * 3*7 is 2^2 * 7 = 28.

Solution 2:

We will begin by calculating the least common multiples, and then we will take their greatest common factor.

Since 14 is divisible by 7, the LCM of 8 and 14 must be a multiple of 8 = 2^3 and 7. Since 2^3 and 7 are powers of distinct primes, any number that is a multiple of both of them must be a multiple of 2^3 * 7 = 56. Note that 56 is a multiple of both 8 and 14, so {LCM}(8, 14) = 56. The prime factorization of 12 is 2^2 * 3, and 7 is prime, so any multiple of both 12 and 7 must include 2^2, 3, and 7 in its prime factorization. It follows that{LCM}(7, 12) = 2^2 * 3 * 7 = 12 * 7 = 84. We now wish to find GCF(56, 84). Looking at the factorizations of 56 and 84 found earlier in this solution, we can observe that 2^2 * 7 = 28 is a factor of both 56 and 84. The only factor of 56 that is larger than 28 is 56, but 56 is not a factor of 84, so {GCF}(56, 84) = 28.

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step-by-step explanation: