Least Common Multiple (LCM) of 59 and 72
The least common multiple (LCM) of 59 and 72 is 4248.
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 59 and 72?
First, calculate the GCD of 59 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 72 = 0 remainder 59 |
| 2 | 72 ÷ 59 = 1 remainder 13 |
| 3 | 59 ÷ 13 = 4 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 54 | 1026 |
| 188 and 169 | 31772 |
| 34 and 167 | 5678 |
| 169 and 39 | 507 |
| 27 and 76 | 2052 |