Least Common Multiple (LCM) of 36 and 99
The least common multiple (LCM) of 36 and 99 is 396.
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 36 and 99?
First, calculate the GCD of 36 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 99 = 0 remainder 36 |
| 2 | 99 ÷ 36 = 2 remainder 27 |
| 3 | 36 ÷ 27 = 1 remainder 9 |
| 4 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 130 | 13910 |
| 120 and 180 | 360 |
| 42 and 107 | 4494 |
| 43 and 99 | 4257 |
| 130 and 13 | 130 |