Least Common Multiple (LCM) of 45 and 159
The least common multiple (LCM) of 45 and 159 is 2385.
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 159?
First, calculate the GCD of 45 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 159 = 0 remainder 45 |
| 2 | 159 ÷ 45 = 3 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 42 | 546 |
| 148 and 169 | 25012 |
| 136 and 165 | 22440 |
| 162 and 108 | 324 |
| 37 and 94 | 3478 |