Least Common Multiple (LCM) of 60 and 99
The least common multiple (LCM) of 60 and 99 is 1980.
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 60 and 99?
First, calculate the GCD of 60 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 99 = 0 remainder 60 |
| 2 | 99 ÷ 60 = 1 remainder 39 |
| 3 | 60 ÷ 39 = 1 remainder 21 |
| 4 | 39 ÷ 21 = 1 remainder 18 |
| 5 | 21 ÷ 18 = 1 remainder 3 |
| 6 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 180 | 1620 |
| 56 and 118 | 3304 |
| 123 and 118 | 14514 |
| 170 and 198 | 16830 |
| 195 and 60 | 780 |