Least Common Multiple (LCM) of 63 and 80
The least common multiple (LCM) of 63 and 80 is 5040.
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 80?
First, calculate the GCD of 63 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 80 = 0 remainder 63 |
| 2 | 80 ÷ 63 = 1 remainder 17 |
| 3 | 63 ÷ 17 = 3 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 122 | 23058 |
| 108 and 185 | 19980 |
| 119 and 86 | 10234 |
| 140 and 112 | 560 |
| 156 and 183 | 9516 |