Least Common Multiple (LCM) of 138 and 178
The least common multiple (LCM) of 138 and 178 is 12282.
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 138 and 178?
First, calculate the GCD of 138 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 178 = 0 remainder 138 |
| 2 | 178 ÷ 138 = 1 remainder 40 |
| 3 | 138 ÷ 40 = 3 remainder 18 |
| 4 | 40 ÷ 18 = 2 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 56 | 952 |
| 180 and 69 | 4140 |
| 70 and 62 | 2170 |
| 101 and 198 | 19998 |
| 170 and 97 | 16490 |