Least Common Multiple (LCM) of 99 and 61
The least common multiple (LCM) of 99 and 61 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 99 and 61?
First, calculate the GCD of 99 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 61 = 1 remainder 38 |
| 2 | 61 ÷ 38 = 1 remainder 23 |
| 3 | 38 ÷ 23 = 1 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 57 | 1482 |
| 106 and 67 | 7102 |
| 135 and 120 | 1080 |
| 146 and 46 | 3358 |
| 164 and 159 | 26076 |