Least Common Multiple (LCM) of 180 and 99
The least common multiple (LCM) of 180 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 180 and 99?
First, calculate the GCD of 180 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 99 = 1 remainder 81 |
| 2 | 99 ÷ 81 = 1 remainder 18 |
| 3 | 81 ÷ 18 = 4 remainder 9 |
| 4 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 78 | 13650 |
| 143 and 31 | 4433 |
| 123 and 117 | 4797 |
| 89 and 111 | 9879 |
| 136 and 70 | 4760 |