Least Common Multiple (LCM) of 150 and 182
The least common multiple (LCM) of 150 and 182 is 13650.
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 182?
First, calculate the GCD of 150 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 182 = 0 remainder 150 |
| 2 | 182 ÷ 150 = 1 remainder 32 |
| 3 | 150 ÷ 32 = 4 remainder 22 |
| 4 | 32 ÷ 22 = 1 remainder 10 |
| 5 | 22 ÷ 10 = 2 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 50 | 5850 |
| 81 and 174 | 4698 |
| 142 and 68 | 4828 |
| 96 and 43 | 4128 |
| 173 and 121 | 20933 |