Least Common Multiple (LCM) of 63 and 177
The least common multiple (LCM) of 63 and 177 is 3717.
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 63 and 177?
First, calculate the GCD of 63 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 177 = 0 remainder 63 |
| 2 | 177 ÷ 63 = 2 remainder 51 |
| 3 | 63 ÷ 51 = 1 remainder 12 |
| 4 | 51 ÷ 12 = 4 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 120 | 2040 |
| 117 and 44 | 5148 |
| 189 and 103 | 19467 |
| 135 and 152 | 20520 |
| 77 and 159 | 12243 |