GCD & LCM Calculator

Step-by-step solution

1. 1

   Start

   Find gcd(252, 105) with the Euclidean algorithm: divide, keep the remainder, repeat until the remainder is 0.

   $$\gcd(252,\, 105)$$
2. 2

   Division step 1

   Divide 252 by 105 and keep the remainder 42 — it becomes the next divisor.

   $$252 = 2 \cdot 105 + 42$$
3. 3

   Division step 2

   Divide 105 by 42 and keep the remainder 21 — it becomes the next divisor.

   $$105 = 2 \cdot 42 + 21$$
4. 4

   Division step 3

   21 divides 42 exactly, so the algorithm stops here.

   $$42 = 2 \cdot 21 + 0$$
5. 5

   The gcd is the last non-zero remainder

   The remainders shrink until they hit 0; the last divisor, 21, is the gcd.

   $$\gcd(252,\, 105) = 21$$
6. 6

   From the gcd to the lcm

   For any two numbers, gcd · lcm = abs(a · b). Dividing 252 · 105 by the gcd 21 gives the lcm.

   $$\operatorname{lcm}(252,\, 105) = \frac{252 \cdot 105}{\gcd(252,\, 105)} = \frac{26460}{21} = 1260$$
7. 7

   Result

   gcd(252, 105) = 21 and lcm(252, 105) = 1260