Least Common Multiple (LCM) of 99 and 77
The least common multiple (LCM) of 99 and 77 is 693.
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 77?
First, calculate the GCD of 99 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 77 = 1 remainder 22 |
| 2 | 77 ÷ 22 = 3 remainder 11 |
| 3 | 22 ÷ 11 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 162 | 3078 |
| 188 and 78 | 7332 |
| 51 and 51 | 51 |
| 151 and 54 | 8154 |
| 193 and 104 | 20072 |