Least Common Multiple (LCM) of 97 and 140
The least common multiple (LCM) of 97 and 140 is 13580.
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 140?
First, calculate the GCD of 97 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 140 = 0 remainder 97 |
| 2 | 140 ÷ 97 = 1 remainder 43 |
| 3 | 97 ÷ 43 = 2 remainder 11 |
| 4 | 43 ÷ 11 = 3 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 166 | 9462 |
| 115 and 141 | 16215 |
| 32 and 118 | 1888 |
| 20 and 116 | 580 |
| 190 and 109 | 20710 |