if you know the lcm of 4 and 5, how could you find the lcm of 40 and 50
4=2*2
5 = 5
LCM = 2*2*5 = 20
40 = 10*4
50 = 10*5
so I suspect that LCM = 10*20 = 200
check
40 = 10 * 4 = 2 * 5 * 2 * 2
50 = 10 * 5 = 2 * 5 * 5
need 3 twos and two fives
2*2*2 * 5*5 = 8*25 = 200 sure enough
To find the least common multiple (LCM) of 40 and 50, we can use the fact that the LCM of two numbers is equal to the product of the numbers divided by their greatest common divisor (GCD).
1. Find the GCD of 40 and 50:
- One way to find the GCD is by using the Euclidean algorithm. Divide 50 by 40: 50 ÷ 40 = 1 with a remainder of 10.
- Now divide the previous divisor (40) by the remainder (10): 40 ÷ 10 = 4 with no remainder.
- Since there is no remainder, 10 is the GCD of 40 and 50.
2. Calculate the LCM of 40 and 50:
- Use the formula LCM(a, b) = (a * b) / GCD(a, b).
- Substitute the values for a and b: LCM(40, 50) = (40 * 50) / 10 = 200.
Therefore, the LCM of 40 and 50 is 200.