Lcm Pairs 279683

1. The problem asks to find the Least Common Multiple (LCM) of given pairs of numbers: $4$ and $5$, $6$ and $8$, $4$ and $10$, $5$ and $8$, $8$ and $20$. 2. The LCM of two numbers is the smallest positive integer that is divisible by both numbers. 3. To find the LCM, we can use the prime factorization method or the formula: $$\text{LCM}(a,b) = \frac{|a \times b|}{\text{GCD}(a,b)}$$ where GCD is the Greatest Common Divisor. 4. Calculate each pair: - For $4$ and $5$: - $4 = 2^2$ - $5 = 5$ - GCD$(4,5) = 1$ - $$\text{LCM}(4,5) = \frac{4 \times 5}{1} = 20$$ - For $6$ and $8$: - $6 = 2 \times 3$ - $8 = 2^3$ - GCD$(6,8) = 2$ - $$\text{LCM}(6,8) = \frac{6 \times 8}{2} = \frac{48}{2} = 24$$ - For $4$ and $10$: - $4 = 2^2$ - $10 = 2 \times 5$ - GCD$(4,10) = 2$ - $$\text{LCM}(4,10) = \frac{4 \times 10}{2} = \frac{40}{2} = 20$$ - For $5$ and $8$: - $5 = 5$ - $8 = 2^3$ - GCD$(5,8) = 1$ - $$\text{LCM}(5,8) = \frac{5 \times 8}{1} = 40$$ - For $8$ and $20$: - $8 = 2^3$ - $20 = 2^2 \times 5$ - GCD$(8,20) = 4$ - $$\text{LCM}(8,20) = \frac{8 \times 20}{4} = \frac{160}{4} = 40$$ 5. Final answers: - A: $24$ - B: $20$ - C: $40$ - D: $40$