Least Common Multiple (LCM) of 156 and 200
The least common multiple (LCM) of 156 and 200 is 7800.
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 156 and 200?
First, calculate the GCD of 156 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 200 = 0 remainder 156 |
| 2 | 200 ÷ 156 = 1 remainder 44 |
| 3 | 156 ÷ 44 = 3 remainder 24 |
| 4 | 44 ÷ 24 = 1 remainder 20 |
| 5 | 24 ÷ 20 = 1 remainder 4 |
| 6 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 93 | 5394 |
| 131 and 167 | 21877 |
| 42 and 25 | 1050 |
| 71 and 21 | 1491 |
| 159 and 144 | 7632 |