Least Common Multiple (LCM) of 139 and 74
The least common multiple (LCM) of 139 and 74 is 10286.
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 74?
First, calculate the GCD of 139 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 74 = 1 remainder 65 |
| 2 | 74 ÷ 65 = 1 remainder 9 |
| 3 | 65 ÷ 9 = 7 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 150 | 3450 |
| 74 and 113 | 8362 |
| 115 and 186 | 21390 |
| 40 and 169 | 6760 |
| 74 and 155 | 11470 |