Least Common Multiple (LCM) of 138 and 179
The least common multiple (LCM) of 138 and 179 is 24702.
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 179?
First, calculate the GCD of 138 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 179 = 0 remainder 138 |
| 2 | 179 ÷ 138 = 1 remainder 41 |
| 3 | 138 ÷ 41 = 3 remainder 15 |
| 4 | 41 ÷ 15 = 2 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 70 | 1190 |
| 186 and 156 | 4836 |
| 167 and 23 | 3841 |
| 73 and 100 | 7300 |
| 153 and 193 | 29529 |