Least Common Multiple (LCM) of 97 and 134
The least common multiple (LCM) of 97 and 134 is 12998.
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 134?
First, calculate the GCD of 97 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 134 = 0 remainder 97 |
| 2 | 134 ÷ 97 = 1 remainder 37 |
| 3 | 97 ÷ 37 = 2 remainder 23 |
| 4 | 37 ÷ 23 = 1 remainder 14 |
| 5 | 23 ÷ 14 = 1 remainder 9 |
| 6 | 14 ÷ 9 = 1 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 68 | 68 |
| 18 and 119 | 2142 |
| 33 and 15 | 165 |
| 171 and 19 | 171 |
| 134 and 44 | 2948 |