Least Common Multiple (LCM) of 150 and 117
The least common multiple (LCM) of 150 and 117 is 5850.
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 117?
First, calculate the GCD of 150 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 117 = 1 remainder 33 |
| 2 | 117 ÷ 33 = 3 remainder 18 |
| 3 | 33 ÷ 18 = 1 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 81 | 810 |
| 88 and 187 | 1496 |
| 143 and 166 | 23738 |
| 68 and 174 | 5916 |
| 59 and 104 | 6136 |