Least Common Multiple (LCM) of 42 and 45
The least common multiple (LCM) of 42 and 45 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 42 and 45?
First, calculate the GCD of 42 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 45 = 0 remainder 42 |
| 2 | 45 ÷ 42 = 1 remainder 3 |
| 3 | 42 ÷ 3 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 64 | 8384 |
| 72 and 104 | 936 |
| 167 and 125 | 20875 |
| 13 and 128 | 1664 |
| 147 and 72 | 3528 |