Least Common Multiple (LCM) of 139 and 172
The least common multiple (LCM) of 139 and 172 is 23908.
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 172?
First, calculate the GCD of 139 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 172 = 0 remainder 139 |
| 2 | 172 ÷ 139 = 1 remainder 33 |
| 3 | 139 ÷ 33 = 4 remainder 7 |
| 4 | 33 ÷ 7 = 4 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 137 | 13974 |
| 85 and 123 | 10455 |
| 130 and 112 | 7280 |
| 170 and 151 | 25670 |
| 126 and 16 | 1008 |