Least Common Multiple (LCM) of 140 and 51
The least common multiple (LCM) of 140 and 51 is 7140.
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 51?
First, calculate the GCD of 140 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 51 = 2 remainder 38 |
| 2 | 51 ÷ 38 = 1 remainder 13 |
| 3 | 38 ÷ 13 = 2 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 42 | 3066 |
| 192 and 44 | 2112 |
| 109 and 94 | 10246 |
| 75 and 75 | 75 |
| 154 and 49 | 1078 |