Least Common Multiple (LCM) of 54 and 139
The least common multiple (LCM) of 54 and 139 is 7506.
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 139?
First, calculate the GCD of 54 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 139 = 0 remainder 54 |
| 2 | 139 ÷ 54 = 2 remainder 31 |
| 3 | 54 ÷ 31 = 1 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 153 | 26775 |
| 74 and 179 | 13246 |
| 15 and 100 | 300 |
| 113 and 138 | 15594 |
| 138 and 132 | 3036 |