Least Common Multiple (LCM) of 99 and 140
The least common multiple (LCM) of 99 and 140 is 13860.
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 140?
First, calculate the GCD of 99 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 140 = 0 remainder 99 |
| 2 | 140 ÷ 99 = 1 remainder 41 |
| 3 | 99 ÷ 41 = 2 remainder 17 |
| 4 | 41 ÷ 17 = 2 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 194 | 36278 |
| 32 and 20 | 160 |
| 143 and 51 | 7293 |
| 81 and 47 | 3807 |
| 40 and 112 | 560 |