Least Common Multiple (LCM) of 30 and 140
The least common multiple (LCM) of 30 and 140 is 420.
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 140?
First, calculate the GCD of 30 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 140 = 0 remainder 30 |
| 2 | 140 ÷ 30 = 4 remainder 20 |
| 3 | 30 ÷ 20 = 1 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 21 | 3192 |
| 164 and 126 | 10332 |
| 30 and 74 | 1110 |
| 72 and 53 | 3816 |
| 95 and 142 | 13490 |