Least Common Multiple (LCM) of 140 and 58
The least common multiple (LCM) of 140 and 58 is 4060.
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 140 and 58?
First, calculate the GCD of 140 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 58 = 2 remainder 24 |
| 2 | 58 ÷ 24 = 2 remainder 10 |
| 3 | 24 ÷ 10 = 2 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 12 | 1068 |
| 67 and 113 | 7571 |
| 74 and 56 | 2072 |
| 178 and 100 | 8900 |
| 42 and 79 | 3318 |