Least Common Multiple (LCM) of 54 and 70
The least common multiple (LCM) of 54 and 70 is 1890.
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 54 and 70?
First, calculate the GCD of 54 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 70 = 0 remainder 54 |
| 2 | 70 ÷ 54 = 1 remainder 16 |
| 3 | 54 ÷ 16 = 3 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 195 | 975 |
| 109 and 87 | 9483 |
| 188 and 51 | 9588 |
| 148 and 30 | 2220 |
| 17 and 112 | 1904 |