HCF and LCM

The Highest Common Factor (HCF) is defined for integers. Since $\pi$ is an irrational number, the concept of HCF between an integer and an irrational number is not defined in standard arithmetic. Therefore, the answer does not exist.

The product of two numbers is equal to the product of their HCF and LCM. Here, 6 * x = 2 * 24. Solving for x gives 48 / 6 = 8. Therefore, the other number is 8.

Let numbers be 13x and 15x. LCM(13x, 15x) = LCM(13,15) x x = 195x = 39780, so x = 204. Numbers are 13x204 = 2652 and 15x204 = 3060. Verification: LCM of 2652 and 3060 is indeed 39780, maintaining the 13:15 ratio.

LCM * HCF = Product of the two numbers LCM of the two numbers is given by: Product of the two numbers/HCF = 2560/16 = 160

Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, 144, 162, ... Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, ... LCM = 126

Prime factorisation of 24 = 2 × 2 × 2 × 3 Prime factorisation of 16 = 2 × 2 × 2 × 2 HCF of 24 and 16 = 2 × 2 × 2 = 8

Multiples of 1 = 1, 2, 3, ... Multiples of 2 = 2, 4, ... LCM of 1 and 2 = 2

Prime factorisation of 56 = 2 × 2 × 2 × 7 Prime factorisation of 40 = 2 × 2 × 2 × 5 HCF of 56 and 40 = 2 × 2 × 2 = 8

Prime factorisation of 16 = 2 × 2 × 2 × 2 Prime factorisation of 32 = 2 × 2 × 2 × 2 × 2 HCF of 16 and 32 = 2 × 2 × 2 × 2 = 16

Prime factorisation of 39 = 3 × 13 Prime factorisation of 65 = 5 × 13 HCF of 39 and 65 = 13

Prime factorisation of 15 = 3 × 5 Prime factorisation of 25 = 5 × 5 HCF of 15 and 25 = 5

Prime factorisation of 27 = 3 × 3 × 3 Prime factorisation of 9 = 3 × 3 HCF of 27 and 9 = 9

Prime factorisation of 14 = 2 × 7 Prime factorisation of 70 = 2 × 7 × 5 HCF of 14 and 70 = 14

Prime factorisation of 51 = 3 × 17 Prime factorisationof 18 = 2 × 3 × 3 HCF of 51 and 18 = 3

Prime factorisation of 1470 = 2 × 3 × 5 × 7 × 7 Prime factorisation of 220 = 2 × 2 × 5 × 11 HCF of 1470 and 220 = 10