Least Common Multiple (LCM) of 187 and 74
The least common multiple (LCM) of 187 and 74 is 13838.
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 187 and 74?
First, calculate the GCD of 187 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 74 = 2 remainder 39 |
| 2 | 74 ÷ 39 = 1 remainder 35 |
| 3 | 39 ÷ 35 = 1 remainder 4 |
| 4 | 35 ÷ 4 = 8 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 67 | 5695 |
| 87 and 101 | 8787 |
| 110 and 46 | 2530 |
| 139 and 76 | 10564 |
| 71 and 109 | 7739 |