Least Common Multiple (LCM) of 150 and 176
The least common multiple (LCM) of 150 and 176 is 13200.
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 176?
First, calculate the GCD of 150 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 176 = 0 remainder 150 |
| 2 | 176 ÷ 150 = 1 remainder 26 |
| 3 | 150 ÷ 26 = 5 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 176 | 1232 |
| 198 and 56 | 5544 |
| 30 and 153 | 1530 |
| 80 and 91 | 7280 |
| 80 and 134 | 5360 |