Least Common Multiple (LCM) of 52 and 150
The least common multiple (LCM) of 52 and 150 is 3900.
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 52 and 150?
First, calculate the GCD of 52 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 150 = 0 remainder 52 |
| 2 | 150 ÷ 52 = 2 remainder 46 |
| 3 | 52 ÷ 46 = 1 remainder 6 |
| 4 | 46 ÷ 6 = 7 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 87 | 16008 |
| 137 and 150 | 20550 |
| 38 and 199 | 7562 |
| 105 and 102 | 3570 |
| 49 and 100 | 4900 |