Least Common Multiple (LCM) of 150 and 114
The least common multiple (LCM) of 150 and 114 is 2850.
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 114?
First, calculate the GCD of 150 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 114 = 1 remainder 36 |
| 2 | 114 ÷ 36 = 3 remainder 6 |
| 3 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 90 | 990 |
| 108 and 195 | 7020 |
| 99 and 175 | 17325 |
| 100 and 42 | 2100 |
| 78 and 169 | 1014 |