Least Common Multiple (LCM) of 97 and 142
The least common multiple (LCM) of 97 and 142 is 13774.
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 142?
First, calculate the GCD of 97 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 142 = 0 remainder 97 |
| 2 | 142 ÷ 97 = 1 remainder 45 |
| 3 | 97 ÷ 45 = 2 remainder 7 |
| 4 | 45 ÷ 7 = 6 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 42 | 1554 |
| 101 and 177 | 17877 |
| 142 and 167 | 23714 |
| 65 and 49 | 3185 |
| 10 and 13 | 130 |