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 |
|---|---|
| 42 and 58 | 1218 |
| 124 and 13 | 1612 |
| 74 and 146 | 5402 |
| 118 and 56 | 3304 |
| 170 and 190 | 3230 |