Least Common Multiple (LCM) of 64 and 112
The least common multiple (LCM) of 64 and 112 is 448.
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 64 and 112?
First, calculate the GCD of 64 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 112 = 0 remainder 64 |
| 2 | 112 ÷ 64 = 1 remainder 48 |
| 3 | 64 ÷ 48 = 1 remainder 16 |
| 4 | 48 ÷ 16 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 141 | 15510 |
| 105 and 39 | 1365 |
| 187 and 171 | 31977 |
| 178 and 121 | 21538 |
| 127 and 129 | 16383 |