Least Common Multiple (LCM) of 30 and 145
The least common multiple (LCM) of 30 and 145 is 870.
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 145?
First, calculate the GCD of 30 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 145 = 0 remainder 30 |
| 2 | 145 ÷ 30 = 4 remainder 25 |
| 3 | 30 ÷ 25 = 1 remainder 5 |
| 4 | 25 ÷ 5 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 148 | 5180 |
| 192 and 67 | 12864 |
| 110 and 23 | 2530 |
| 13 and 81 | 1053 |
| 44 and 106 | 2332 |