Least Common Multiple (LCM) of 55 and 64
The least common multiple (LCM) of 55 and 64 is 3520.
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 55 and 64?
First, calculate the GCD of 55 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 64 = 0 remainder 55 |
| 2 | 64 ÷ 55 = 1 remainder 9 |
| 3 | 55 ÷ 9 = 6 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 170 | 3400 |
| 174 and 71 | 12354 |
| 92 and 185 | 17020 |
| 113 and 176 | 19888 |
| 25 and 141 | 3525 |