Least Common Multiple (LCM) of 97 and 36
The least common multiple (LCM) of 97 and 36 is 3492.
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 36?
First, calculate the GCD of 97 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 36 = 2 remainder 25 |
| 2 | 36 ÷ 25 = 1 remainder 11 |
| 3 | 25 ÷ 11 = 2 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 159 | 10494 |
| 102 and 137 | 13974 |
| 145 and 171 | 24795 |
| 116 and 95 | 11020 |
| 105 and 200 | 4200 |