Least Common Multiple (LCM) of 39 and 140
The least common multiple (LCM) of 39 and 140 is 5460.
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 39 and 140?
First, calculate the GCD of 39 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 140 = 0 remainder 39 |
| 2 | 140 ÷ 39 = 3 remainder 23 |
| 3 | 39 ÷ 23 = 1 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 42 | 924 |
| 107 and 124 | 13268 |
| 119 and 144 | 17136 |
| 91 and 54 | 4914 |
| 121 and 25 | 3025 |