Least Common Multiple (LCM) of 153 and 200
The least common multiple (LCM) of 153 and 200 is 30600.
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 153 and 200?
First, calculate the GCD of 153 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 200 = 0 remainder 153 |
| 2 | 200 ÷ 153 = 1 remainder 47 |
| 3 | 153 ÷ 47 = 3 remainder 12 |
| 4 | 47 ÷ 12 = 3 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 199 | 37412 |
| 180 and 100 | 900 |
| 115 and 197 | 22655 |
| 77 and 106 | 8162 |
| 22 and 134 | 1474 |