Least Common Multiple (LCM) of 54 and 187
The least common multiple (LCM) of 54 and 187 is 10098.
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 54 and 187?
First, calculate the GCD of 54 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 187 = 0 remainder 54 |
| 2 | 187 ÷ 54 = 3 remainder 25 |
| 3 | 54 ÷ 25 = 2 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 137 | 17536 |
| 119 and 174 | 20706 |
| 20 and 89 | 1780 |
| 33 and 74 | 2442 |
| 129 and 160 | 20640 |