Least Common Multiple (LCM) of 58 and 53
The least common multiple (LCM) of 58 and 53 is 3074.
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 58 and 53?
First, calculate the GCD of 58 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 53 = 1 remainder 5 |
| 2 | 53 ÷ 5 = 10 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 160 | 2720 |
| 12 and 163 | 1956 |
| 125 and 152 | 19000 |
| 105 and 45 | 315 |
| 30 and 101 | 3030 |