Least Common Multiple (LCM) of 140 and 99
The least common multiple (LCM) of 140 and 99 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 140 and 99?
First, calculate the GCD of 140 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 99 = 1 remainder 41 |
| 2 | 99 ÷ 41 = 2 remainder 17 |
| 3 | 41 ÷ 17 = 2 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 122 | 14762 |
| 51 and 89 | 4539 |
| 173 and 140 | 24220 |
| 167 and 15 | 2505 |
| 198 and 93 | 6138 |