Least Common Multiple (LCM) of 100 and 187
The least common multiple (LCM) of 100 and 187 is 18700.
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 100 and 187?
First, calculate the GCD of 100 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 187 = 0 remainder 100 |
| 2 | 187 ÷ 100 = 1 remainder 87 |
| 3 | 100 ÷ 87 = 1 remainder 13 |
| 4 | 87 ÷ 13 = 6 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 194 | 1358 |
| 156 and 49 | 7644 |
| 147 and 72 | 3528 |
| 79 and 71 | 5609 |
| 109 and 138 | 15042 |