Least Common Multiple (LCM) of 97 and 64
The least common multiple (LCM) of 97 and 64 is 6208.
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 97 and 64?
First, calculate the GCD of 97 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 64 = 1 remainder 33 |
| 2 | 64 ÷ 33 = 1 remainder 31 |
| 3 | 33 ÷ 31 = 1 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 123 | 14637 |
| 62 and 123 | 7626 |
| 157 and 130 | 20410 |
| 70 and 81 | 5670 |
| 129 and 128 | 16512 |