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Find the LCM of the following sets of numbers: a) 8 and 6, d) 48 and 32, g) 25, 30 and 45.

Mathematics

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Answers

3 parts
a
24
d
96
g
450

Step-by-step solution

6 steps

Here are the LCMs for the visible parts of the question:

Part a· 2 steps

Find the LCM of 8 and 6.

  1. Find the prime factorization of each number.

    8=2×2×2=238 = 2 \times 2 \times 2 = 2^3 6=2×36 = 2 \times 3
  2. Identify all prime factors and take the highest power of each.

    LCM(8,6)=23×31=8×3=24\text{LCM}(8, 6) = 2^3 \times 3^1 = 8 \times 3 = 24

    The LCM of 8 and 6 is 24\boxed{24}.

Part d96

Find the LCM of 48 and 32.

  1. Find the prime factorization of each number.

    48=2×2×2×2×3=24×348 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3 32=2×2×2×2×2=2532 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5
  2. Identify all prime factors and take the highest power of each.

    LCM(48,32)=25×31=32×3=96\text{LCM}(48, 32) = 2^5 \times 3^1 = 32 \times 3 = 96

    The LCM of 48 and 32 is 96\boxed{96}.

Part g450

Find the LCM of 25, 30 and 45.

  1. Find the prime factorization of each number.

    25=5×5=5225 = 5 \times 5 = 5^2 30=2×3×530 = 2 \times 3 \times 5 45=3×3×5=32×545 = 3 \times 3 \times 5 = 3^2 \times 5
  2. Identify all prime factors and take the highest power of each.

    LCM(25,30,45)=21×32×52=2×9×25=18×25=450\text{LCM}(25, 30, 45) = 2^1 \times 3^2 \times 5^2 = 2 \times 9 \times 25 = 18 \times 25 = 450

    The LCM of 25, 30 and 45 is 450\boxed{450}.

    Parts (b), (e), and (h) are incomplete in the image.

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