Least Common Multiple (LCM) of 45 and 12
The least common multiple (LCM) of 45 and 12 is 180.
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 12?
First, calculate the GCD of 45 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 12 = 3 remainder 9 |
| 2 | 12 ÷ 9 = 1 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 10 | 230 |
| 135 and 176 | 23760 |
| 22 and 142 | 1562 |
| 31 and 29 | 899 |
| 89 and 24 | 2136 |