Least Common Multiple (LCM) of 140 and 102
The least common multiple (LCM) of 140 and 102 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 102?
First, calculate the GCD of 140 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 102 = 1 remainder 38 |
| 2 | 102 ÷ 38 = 2 remainder 26 |
| 3 | 38 ÷ 26 = 1 remainder 12 |
| 4 | 26 ÷ 12 = 2 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 140 | 1120 |
| 117 and 43 | 5031 |
| 112 and 30 | 1680 |
| 145 and 177 | 25665 |
| 102 and 126 | 2142 |