Least Common Multiple (LCM) of 34 and 97
The least common multiple (LCM) of 34 and 97 is 3298.
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 34 and 97?
First, calculate the GCD of 34 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 97 = 0 remainder 34 |
| 2 | 97 ÷ 34 = 2 remainder 29 |
| 3 | 34 ÷ 29 = 1 remainder 5 |
| 4 | 29 ÷ 5 = 5 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 60 | 60 |
| 45 and 67 | 3015 |
| 104 and 30 | 1560 |
| 96 and 35 | 3360 |
| 82 and 101 | 8282 |