
Least Common Multiple (LCM) of 72 and 100
The least common multiple (LCM) of 72 and 100 is 1800.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 72 and 100?
First, calculate the GCD of 72 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 72 ÷ 100 = 0 remainder 72 |
2 | 100 ÷ 72 = 1 remainder 28 |
3 | 72 ÷ 28 = 2 remainder 16 |
4 | 28 ÷ 16 = 1 remainder 12 |
5 | 16 ÷ 12 = 1 remainder 4 |
6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
141 and 117 | 5499 |
58 and 139 | 8062 |
55 and 193 | 10615 |
166 and 83 | 166 |
196 and 29 | 5684 |