Least Common Multiple (LCM) of 140 and 74
The least common multiple (LCM) of 140 and 74 is 5180.
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 74?
First, calculate the GCD of 140 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 74 = 1 remainder 66 |
| 2 | 74 ÷ 66 = 1 remainder 8 |
| 3 | 66 ÷ 8 = 8 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 77 | 1001 |
| 98 and 113 | 11074 |
| 133 and 97 | 12901 |
| 129 and 51 | 2193 |
| 73 and 141 | 10293 |