Least Common Multiple (LCM) of 139 and 178
The least common multiple (LCM) of 139 and 178 is 24742.
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 139 and 178?
First, calculate the GCD of 139 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 178 = 0 remainder 139 |
| 2 | 178 ÷ 139 = 1 remainder 39 |
| 3 | 139 ÷ 39 = 3 remainder 22 |
| 4 | 39 ÷ 22 = 1 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 58 | 2842 |
| 144 and 64 | 576 |
| 99 and 88 | 792 |
| 87 and 14 | 1218 |
| 102 and 25 | 2550 |