Least Common Multiple (LCM) of 99 and 150
The least common multiple (LCM) of 99 and 150 is 4950.
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 99 and 150?
First, calculate the GCD of 99 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 150 = 0 remainder 99 |
| 2 | 150 ÷ 99 = 1 remainder 51 |
| 3 | 99 ÷ 51 = 1 remainder 48 |
| 4 | 51 ÷ 48 = 1 remainder 3 |
| 5 | 48 ÷ 3 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 29 | 4350 |
| 78 and 118 | 4602 |
| 105 and 75 | 525 |
| 199 and 176 | 35024 |
| 133 and 39 | 5187 |