Least Common Multiple (LCM) of 30 and 141
The least common multiple (LCM) of 30 and 141 is 1410.
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 30 and 141?
First, calculate the GCD of 30 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 141 = 0 remainder 30 |
| 2 | 141 ÷ 30 = 4 remainder 21 |
| 3 | 30 ÷ 21 = 1 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 43 | 8428 |
| 52 and 182 | 364 |
| 66 and 35 | 2310 |
| 112 and 90 | 5040 |
| 118 and 131 | 15458 |