Least Common Multiple (LCM) of 124 and 178
The least common multiple (LCM) of 124 and 178 is 11036.
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 124 and 178?
First, calculate the GCD of 124 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 124 ÷ 178 = 0 remainder 124 |
| 2 | 178 ÷ 124 = 1 remainder 54 |
| 3 | 124 ÷ 54 = 2 remainder 16 |
| 4 | 54 ÷ 16 = 3 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 38 | 114 |
| 20 and 51 | 1020 |
| 124 and 21 | 2604 |
| 180 and 95 | 3420 |
| 171 and 91 | 15561 |