Least Common Multiple (LCM) of 45 and 171
The least common multiple (LCM) of 45 and 171 is 855.
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 171?
First, calculate the GCD of 45 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 171 = 0 remainder 45 |
| 2 | 171 ÷ 45 = 3 remainder 36 |
| 3 | 45 ÷ 36 = 1 remainder 9 |
| 4 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 185 | 12210 |
| 186 and 29 | 5394 |
| 28 and 188 | 1316 |
| 64 and 117 | 7488 |
| 109 and 127 | 13843 |