Least Common Multiple (LCM) of 45 and 42
The least common multiple (LCM) of 45 and 42 is 630.
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 42?
First, calculate the GCD of 45 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 42 = 1 remainder 3 |
| 2 | 42 ÷ 3 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 10 | 310 |
| 179 and 116 | 20764 |
| 36 and 15 | 180 |
| 112 and 174 | 9744 |
| 31 and 49 | 1519 |