Least Common Multiple (LCM) of 64 and 97
The least common multiple (LCM) of 64 and 97 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 64 and 97?
First, calculate the GCD of 64 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 97 = 0 remainder 64 |
| 2 | 97 ÷ 64 = 1 remainder 33 |
| 3 | 64 ÷ 33 = 1 remainder 31 |
| 4 | 33 ÷ 31 = 1 remainder 2 |
| 5 | 31 ÷ 2 = 15 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 88 | 13640 |
| 17 and 149 | 2533 |
| 29 and 175 | 5075 |
| 113 and 114 | 12882 |
| 97 and 176 | 17072 |