Least Common Multiple (LCM) of 105 and 142
The least common multiple (LCM) of 105 and 142 is 14910.
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 142?
First, calculate the GCD of 105 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 142 = 0 remainder 105 |
| 2 | 142 ÷ 105 = 1 remainder 37 |
| 3 | 105 ÷ 37 = 2 remainder 31 |
| 4 | 37 ÷ 31 = 1 remainder 6 |
| 5 | 31 ÷ 6 = 5 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 59 | 2537 |
| 171 and 118 | 20178 |
| 125 and 130 | 3250 |
| 37 and 62 | 2294 |
| 138 and 87 | 4002 |