Least Common Multiple (LCM) of 100 and 150
The least common multiple (LCM) of 100 and 150 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 100 and 150?
First, calculate the GCD of 100 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 150 = 0 remainder 100 |
| 2 | 150 ÷ 100 = 1 remainder 50 |
| 3 | 100 ÷ 50 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 137 | 5754 |
| 174 and 195 | 11310 |
| 108 and 22 | 1188 |
| 103 and 87 | 8961 |
| 147 and 71 | 10437 |