Least Common Multiple (LCM) of 99 and 76
The least common multiple (LCM) of 99 and 76 is 7524.
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 76?
First, calculate the GCD of 99 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 76 = 1 remainder 23 |
| 2 | 76 ÷ 23 = 3 remainder 7 |
| 3 | 23 ÷ 7 = 3 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 91 | 1820 |
| 159 and 42 | 2226 |
| 132 and 58 | 3828 |
| 45 and 45 | 45 |
| 185 and 35 | 1295 |