Least Common Multiple (LCM) of 51 and 70
The least common multiple (LCM) of 51 and 70 is 3570.
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 51 and 70?
First, calculate the GCD of 51 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 70 = 0 remainder 51 |
| 2 | 70 ÷ 51 = 1 remainder 19 |
| 3 | 51 ÷ 19 = 2 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 134 | 11658 |
| 104 and 120 | 1560 |
| 128 and 113 | 14464 |
| 15 and 140 | 420 |
| 102 and 151 | 15402 |