Least Common Multiple (LCM) of 139 and 72
The least common multiple (LCM) of 139 and 72 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 139 and 72?
First, calculate the GCD of 139 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 72 = 1 remainder 67 |
| 2 | 72 ÷ 67 = 1 remainder 5 |
| 3 | 67 ÷ 5 = 13 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 103 | 13699 |
| 122 and 122 | 122 |
| 120 and 121 | 14520 |
| 57 and 194 | 11058 |
| 198 and 174 | 5742 |