Least Common Multiple (LCM) of 72 and 139
The least common multiple (LCM) of 72 and 139 is 10008.
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 72 and 139?
First, calculate the GCD of 72 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 139 = 0 remainder 72 |
| 2 | 139 ÷ 72 = 1 remainder 67 |
| 3 | 72 ÷ 67 = 1 remainder 5 |
| 4 | 67 ÷ 5 = 13 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 115 | 13340 |
| 157 and 78 | 12246 |
| 75 and 12 | 300 |
| 70 and 196 | 980 |
| 187 and 165 | 2805 |