Least Common Multiple (LCM) of 97 and 136
The least common multiple (LCM) of 97 and 136 is 13192.
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 136?
First, calculate the GCD of 97 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 136 = 0 remainder 97 |
| 2 | 136 ÷ 97 = 1 remainder 39 |
| 3 | 97 ÷ 39 = 2 remainder 19 |
| 4 | 39 ÷ 19 = 2 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 132 | 4620 |
| 47 and 96 | 4512 |
| 73 and 174 | 12702 |
| 23 and 196 | 4508 |
| 187 and 99 | 1683 |