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 |
|---|---|
| 200 and 188 | 9400 |
| 98 and 105 | 1470 |
| 61 and 23 | 1403 |
| 125 and 81 | 10125 |
| 84 and 196 | 588 |