Least Common Multiple (LCM) of 35 and 97
The least common multiple (LCM) of 35 and 97 is 3395.
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 35 and 97?
First, calculate the GCD of 35 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 97 = 0 remainder 35 |
| 2 | 97 ÷ 35 = 2 remainder 27 |
| 3 | 35 ÷ 27 = 1 remainder 8 |
| 4 | 27 ÷ 8 = 3 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 62 | 992 |
| 199 and 98 | 19502 |
| 78 and 192 | 2496 |
| 30 and 20 | 60 |
| 44 and 83 | 3652 |