Least Common Multiple (LCM) of 99 and 141
The least common multiple (LCM) of 99 and 141 is 4653.
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 141?
First, calculate the GCD of 99 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 141 = 0 remainder 99 |
| 2 | 141 ÷ 99 = 1 remainder 42 |
| 3 | 99 ÷ 42 = 2 remainder 15 |
| 4 | 42 ÷ 15 = 2 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 144 | 24336 |
| 21 and 52 | 1092 |
| 83 and 123 | 10209 |
| 32 and 75 | 2400 |
| 184 and 15 | 2760 |