Least Common Multiple (LCM) of 21 and 177
The least common multiple (LCM) of 21 and 177 is 1239.
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 21 and 177?
First, calculate the GCD of 21 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 177 = 0 remainder 21 |
| 2 | 177 ÷ 21 = 8 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 78 | 15522 |
| 111 and 105 | 3885 |
| 134 and 100 | 6700 |
| 177 and 138 | 8142 |
| 138 and 58 | 4002 |