Least Common Multiple (LCM) of 21 and 64
The least common multiple (LCM) of 21 and 64 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 21 and 64?
First, calculate the GCD of 21 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 64 = 0 remainder 21 |
| 2 | 64 ÷ 21 = 3 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 128 | 3456 |
| 195 and 78 | 390 |
| 114 and 113 | 12882 |
| 130 and 91 | 910 |
| 139 and 159 | 22101 |