Least Common Multiple (LCM) of 64 and 84
The least common multiple (LCM) of 64 and 84 is 1344.
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 84?
First, calculate the GCD of 64 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 84 = 0 remainder 64 |
| 2 | 84 ÷ 64 = 1 remainder 20 |
| 3 | 64 ÷ 20 = 3 remainder 4 |
| 4 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 113 | 3390 |
| 96 and 188 | 4512 |
| 89 and 177 | 15753 |
| 104 and 71 | 7384 |
| 140 and 129 | 18060 |