Least Common Multiple (LCM) of 99 and 142
The least common multiple (LCM) of 99 and 142 is 14058.
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 99 and 142?
First, calculate the GCD of 99 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 142 = 0 remainder 99 |
| 2 | 142 ÷ 99 = 1 remainder 43 |
| 3 | 99 ÷ 43 = 2 remainder 13 |
| 4 | 43 ÷ 13 = 3 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 185 | 31635 |
| 90 and 188 | 8460 |
| 195 and 44 | 8580 |
| 71 and 50 | 3550 |
| 135 and 20 | 540 |