Least Common Multiple (LCM) of 140 and 153
The least common multiple (LCM) of 140 and 153 is 21420.
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 153?
First, calculate the GCD of 140 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 153 = 0 remainder 140 |
| 2 | 153 ÷ 140 = 1 remainder 13 |
| 3 | 140 ÷ 13 = 10 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 160 | 3360 |
| 33 and 122 | 4026 |
| 104 and 54 | 2808 |
| 198 and 186 | 6138 |
| 37 and 62 | 2294 |