Least Common Multiple (LCM) of 150 and 178
The least common multiple (LCM) of 150 and 178 is 13350.
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 178?
First, calculate the GCD of 150 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 178 = 0 remainder 150 |
| 2 | 178 ÷ 150 = 1 remainder 28 |
| 3 | 150 ÷ 28 = 5 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 143 | 14729 |
| 183 and 116 | 21228 |
| 83 and 77 | 6391 |
| 67 and 134 | 134 |
| 182 and 139 | 25298 |