Least Common Multiple (LCM) of 97 and 35
The least common multiple (LCM) of 97 and 35 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 97 and 35?
First, calculate the GCD of 97 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 35 = 2 remainder 27 |
| 2 | 35 ÷ 27 = 1 remainder 8 |
| 3 | 27 ÷ 8 = 3 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 110 | 9130 |
| 160 and 106 | 8480 |
| 109 and 125 | 13625 |
| 81 and 92 | 7452 |
| 10 and 175 | 350 |