Least Common Multiple (LCM) of 61 and 99
The least common multiple (LCM) of 61 and 99 is 6039.
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 61 and 99?
First, calculate the GCD of 61 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 99 = 0 remainder 61 |
| 2 | 99 ÷ 61 = 1 remainder 38 |
| 3 | 61 ÷ 38 = 1 remainder 23 |
| 4 | 38 ÷ 23 = 1 remainder 15 |
| 5 | 23 ÷ 15 = 1 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 85 | 850 |
| 45 and 21 | 315 |
| 138 and 43 | 5934 |
| 129 and 188 | 24252 |
| 31 and 198 | 6138 |