Least Common Multiple (LCM) of 45 and 187
The least common multiple (LCM) of 45 and 187 is 8415.
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 45 and 187?
First, calculate the GCD of 45 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 187 = 0 remainder 45 |
| 2 | 187 ÷ 45 = 4 remainder 7 |
| 3 | 45 ÷ 7 = 6 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 136 | 22440 |
| 105 and 56 | 840 |
| 175 and 129 | 22575 |
| 12 and 156 | 156 |
| 42 and 21 | 42 |