Least Common Multiple (LCM) of 63 and 180
The least common multiple (LCM) of 63 and 180 is 1260.
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 180?
First, calculate the GCD of 63 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 180 = 0 remainder 63 |
| 2 | 180 ÷ 63 = 2 remainder 54 |
| 3 | 63 ÷ 54 = 1 remainder 9 |
| 4 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 166 | 17098 |
| 35 and 109 | 3815 |
| 176 and 174 | 15312 |
| 106 and 15 | 1590 |
| 127 and 84 | 10668 |