Least Common Multiple (LCM) of 105 and 42
The least common multiple (LCM) of 105 and 42 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 105 and 42?
First, calculate the GCD of 105 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 42 = 2 remainder 21 |
| 2 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 90 | 10710 |
| 95 and 190 | 190 |
| 121 and 191 | 23111 |
| 17 and 70 | 1190 |
| 96 and 177 | 5664 |