Least Common Multiple (LCM) of 30 and 154
The least common multiple (LCM) of 30 and 154 is 2310.
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 154?
First, calculate the GCD of 30 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 154 = 0 remainder 30 |
| 2 | 154 ÷ 30 = 5 remainder 4 |
| 3 | 30 ÷ 4 = 7 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 165 | 23430 |
| 170 and 92 | 7820 |
| 186 and 107 | 19902 |
| 43 and 80 | 3440 |
| 63 and 121 | 7623 |