Least Common Multiple (LCM) of 72 and 200
The least common multiple (LCM) of 72 and 200 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 200?
First, calculate the GCD of 72 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 200 = 0 remainder 72 |
| 2 | 200 ÷ 72 = 2 remainder 56 |
| 3 | 72 ÷ 56 = 1 remainder 16 |
| 4 | 56 ÷ 16 = 3 remainder 8 |
| 5 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 129 | 2580 |
| 127 and 184 | 23368 |
| 53 and 101 | 5353 |
| 17 and 53 | 901 |
| 89 and 30 | 2670 |