Least Common Multiple (LCM) of 30 and 42
The least common multiple (LCM) of 30 and 42 is 210.
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 42?
First, calculate the GCD of 30 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 42 = 0 remainder 30 |
| 2 | 42 ÷ 30 = 1 remainder 12 |
| 3 | 30 ÷ 12 = 2 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 36 | 396 |
| 152 and 91 | 13832 |
| 184 and 99 | 18216 |
| 102 and 161 | 16422 |
| 173 and 71 | 12283 |