using prime factorization to find the lcm and gcf\n1) 24, 3\n2) 10, 8\n3) 12, 8\n4) 14, 2\n5) 21, 12\n6) 24…

using prime factorization to find the lcm and gcf\n1) 24, 3\n2) 10, 8\n3) 12, 8\n4) 14, 2\n5) 21, 12\n6) 24, 20\n7) 14, 20\n8) 12, 14\n9) 6, 24\n10) 27, 3\n11) 5, 18\n12) 10, 12

using prime factorization to find the lcm and gcf\n1) 24, 3\n2) 10, 8\n3) 12, 8\n4) 14, 2\n5) 21, 12\n6) 24, 20\n7) 14, 20\n8) 12, 14\n9) 6, 24\n10) 27, 3\n11) 5, 18\n12) 10, 12

Answer

Explanation:

Step1: Prime - factorize the numbers

For two numbers (a) and (b), first find their prime - factorizations. The GCF is the product of the common prime factors with the lowest exponents, and the LCM is the product of all prime factors with the highest exponents.

Step2: Calculate GCF and LCM for each pair

Pair (2) 10 and 8

  • Prime - factorize: (10 = 2\times5), (8 = 2^{3}).
    • GCF: The common prime factor is 2, so (GCF(10,8)=2).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{3}), and for 5, it is (5^{1}). So (LCM(10,8)=2^{3}\times5 = 40).

Pair (3) 12 and 8

  • Prime - factorize: (12 = 2^{2}\times3), (8 = 2^{3}).
    • GCF: The common prime factor is 2 with the lowest power of 2, so (GCF(12,8)=4).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{3}), and for 3, it is (3^{1}). So (LCM(12,8)=2^{3}\times3 = 24).

Pair (4) 14 and 2

  • Prime - factorize: (14 = 2\times7), (2 = 2^{1}).
    • GCF: The common prime factor is 2, so (GCF(14,2)=2).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{1}), and for 7, it is (7^{1}). So (LCM(14,2)=14).

Pair (5) 21 and 12

  • Prime - factorize: (21 = 3\times7), (12 = 2^{2}\times3).
    • GCF: The common prime factor is 3, so (GCF(21,12)=3).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{2}), for 3, it is (3^{1}), and for 7, it is (7^{1}). So (LCM(21,12)=2^{2}\times3\times7 = 84).

Pair (6) 24 and 20

  • Prime - factorize: (24 = 2^{3}\times3), (20 = 2^{2}\times5).
    • GCF: The common prime factor is 2 with the lowest power of 2, so (GCF(24,20)=4).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{3}), for 3, it is (3^{1}), and for 5, it is (5^{1}). So (LCM(24,20)=2^{3}\times3\times5 = 120).

Pair (7) 14 and 20

  • Prime - factorize: (14 = 2\times7), (20 = 2^{2}\times5).
    • GCF: The common prime factor is 2, so (GCF(14,20)=2).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{2}), for 5, it is (5^{1}), and for 7, it is (7^{1}). So (LCM(14,20)=2^{2}\times5\times7 = 140).

Pair (8) 12 and 14

  • Prime - factorize: (12 = 2^{2}\times3), (14 = 2\times7).
    • GCF: The common prime factor is 2, so (GCF(12,14)=2).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{2}), for 3, it is (3^{1}), and for 7, it is (7^{1}). So (LCM(12,14)=2^{2}\times3\times7 = 84).

Pair (9) 6 and 24

  • Prime - factorize: (6 = 2\times3), (24 = 2^{3}\times3).
    • GCF: The common prime factors are 2 and 3 with the lowest powers, so (GCF(6,24)=6).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{3}), and for 3, it is (3^{1}). So (LCM(6,24)=24).

Pair (10) 27 and 3

  • Prime - factorize: (27 = 3^{3}), (3 = 3^{1}).
    • GCF: The common prime factor is 3, so (GCF(27,3)=3).
    • LCM: Take the highest power of each prime factor. For 3, the highest power is (3^{3}), so (LCM(27,3)=27).

Pair (11) 5 and 18

  • Prime - factorize: (5 = 5^{1}), (18 = 2\times3^{2}).
    • GCF: Since there are no common prime factors other than 1, (GCF(5,18)=1).
    • LCM: Take the highest power of each prime factor. For 2, it is (2^{1}), for 3, it is (3^{2}), and for 5, it is (5^{1}). So (LCM(5,18)=2\times3^{2}\times5 = 90).

Pair (12) 10 and 12

  • Prime - factorize: (10 = 2\times5), (12 = 2^{2}\times3).
    • GCF: The common prime factor is 2, so (GCF(10,12)=2).
    • LCM: Take the highest power of each prime factor. For 2, the highest power is (2^{2}), for 3, it is (3^{1}), and for 5, it is (5^{1}). So (LCM(10,12)=60).

Answer:

Pair LCM GCF
10, 8 40 2
12, 8 24 4
14, 2 14 2
21, 12 84 3
24, 20 120 4
14, 20 140 2
12, 14 84 2
6, 24 24 6
27, 3 27 3
5, 18 90 1
10, 12 60 2