Least Common Multiple (LCM) of 42 and 97
The least common multiple (LCM) of 42 and 97 is 4074.
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 42 and 97?
First, calculate the GCD of 42 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 97 = 0 remainder 42 |
| 2 | 97 ÷ 42 = 2 remainder 13 |
| 3 | 42 ÷ 13 = 3 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 188 | 4700 |
| 170 and 89 | 15130 |
| 68 and 143 | 9724 |
| 134 and 114 | 7638 |
| 101 and 109 | 11009 |