Least Common Multiple (LCM) of 140 and 151
The least common multiple (LCM) of 140 and 151 is 21140.
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 151?
First, calculate the GCD of 140 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 151 = 0 remainder 140 |
| 2 | 151 ÷ 140 = 1 remainder 11 |
| 3 | 140 ÷ 11 = 12 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 70 | 210 |
| 139 and 149 | 20711 |
| 109 and 144 | 15696 |
| 191 and 87 | 16617 |
| 129 and 176 | 22704 |