Least Common Multiple (LCM) of 99 and 114
The least common multiple (LCM) of 99 and 114 is 3762.
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 114?
First, calculate the GCD of 99 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 114 = 0 remainder 99 |
| 2 | 114 ÷ 99 = 1 remainder 15 |
| 3 | 99 ÷ 15 = 6 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 69 | 2553 |
| 195 and 66 | 4290 |
| 134 and 164 | 10988 |
| 182 and 57 | 10374 |
| 183 and 156 | 9516 |