Least Common Multiple (LCM) of 56 and 76
The least common multiple (LCM) of 56 and 76 is 1064.
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 56 and 76?
First, calculate the GCD of 56 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 76 = 0 remainder 56 |
| 2 | 76 ÷ 56 = 1 remainder 20 |
| 3 | 56 ÷ 20 = 2 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 80 | 1040 |
| 168 and 109 | 18312 |
| 149 and 96 | 14304 |
| 132 and 152 | 5016 |
| 160 and 122 | 9760 |