Least Common Multiple (LCM) of 42 and 108
The least common multiple (LCM) of 42 and 108 is 756.
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 108?
First, calculate the GCD of 42 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 108 = 0 remainder 42 |
| 2 | 108 ÷ 42 = 2 remainder 24 |
| 3 | 42 ÷ 24 = 1 remainder 18 |
| 4 | 24 ÷ 18 = 1 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 67 | 2546 |
| 186 and 170 | 15810 |
| 15 and 45 | 45 |
| 122 and 62 | 3782 |
| 102 and 40 | 2040 |