Least Common Multiple (LCM) of 150 and 100
The least common multiple (LCM) of 150 and 100 is 300.
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 150 and 100?
First, calculate the GCD of 150 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 100 = 1 remainder 50 |
| 2 | 100 ÷ 50 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 54 | 1026 |
| 42 and 135 | 1890 |
| 81 and 99 | 891 |
| 92 and 99 | 9108 |
| 173 and 68 | 11764 |