Least Common Multiple (LCM) of 104 and 64
The least common multiple (LCM) of 104 and 64 is 832.
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 104 and 64?
First, calculate the GCD of 104 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 64 = 1 remainder 40 |
| 2 | 64 ÷ 40 = 1 remainder 24 |
| 3 | 40 ÷ 24 = 1 remainder 16 |
| 4 | 24 ÷ 16 = 1 remainder 8 |
| 5 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 48 | 1968 |
| 20 and 142 | 1420 |
| 172 and 191 | 32852 |
| 10 and 140 | 140 |
| 117 and 156 | 468 |