Least Common Multiple (LCM) of 42 and 105
The least common multiple (LCM) of 42 and 105 is 210.
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 105?
First, calculate the GCD of 42 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 105 = 0 remainder 42 |
| 2 | 105 ÷ 42 = 2 remainder 21 |
| 3 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 60 | 660 |
| 126 and 175 | 3150 |
| 120 and 184 | 2760 |
| 68 and 11 | 748 |
| 40 and 108 | 1080 |