Least Common Multiple (LCM) of 67 and 99
The least common multiple (LCM) of 67 and 99 is 6633.
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 67 and 99?
First, calculate the GCD of 67 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 99 = 0 remainder 67 |
| 2 | 99 ÷ 67 = 1 remainder 32 |
| 3 | 67 ÷ 32 = 2 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 54 | 7506 |
| 84 and 32 | 672 |
| 25 and 85 | 425 |
| 94 and 119 | 11186 |
| 172 and 100 | 4300 |