LCM and HCF

The LCM of 4 and 6 is the smallest number that both 4 and 6 divide into without leaving a remainder. The multiples of 4 are 4, 8, 12, 16, 20,... and the multiples of 6 are 6, 12, 18, 24,... The smallest common multiple is 12.

The HCF of 18 and 24 is the largest number that divides both of them without leaving a remainder. The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common factor is 6.

The LCM of 3, 4, and 6 is the smallest number that is a multiple of all three numbers. The multiples of 3 are 3, 6, 9, 12, 15,...; the multiples of 4 are 4, 8, 12, 16,...; and the multiples of 6 are 6, 12, 18,... The smallest common multiple is 12.

The LCM of 8 and 10 is the smallest number that both 8 and 10 divide into without leaving a remainder. The multiples of 8 are 8, 16, 24, 32, 40,... and the multiples of 10 are 10, 20, 30, 40,... The smallest common multiple is 40.

The LCM of 4, 5, and 6 is the smallest number that is a multiple of all three numbers. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60,...; the multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...; and the multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,... The smallest common multiple is 60.

The smallest number that is a multiple of both 7 and 3 is the LCM of 7 and 3. The multiples of 7 are 7, 14, 21, 28,... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21,... The smallest common multiple is 21.

The LCM of 5, 10, and 15 is the smallest number that is a multiple of all three numbers. The multiples of 5 are 5, 10, 15, 20, 25, 30,...; the multiples of 10 are 10, 20, 30,...; and the multiples of 15 are 15, 30, 45,... The smallest common multiple is 30.

The HCF of 8 and 12 is the largest number that divides both of them without leaving a remainder. The factors of 8 are 1, 2, 4, 8 and the factors of 12 are 1, 2, 3, 4, 6, 12. The greatest common factor is 4.

The HCF of 14 and 49 is the largest number that divides both of them without leaving a remainder. The factors of 14 are 1, 2, 7, 14 and the factors of 49 are 1, 7, 49. The greatest common factor is 7.

The HCF of 9 and 27 is the largest number that divides both of them without leaving a remainder. The factors of 9 are 1, 3, 9 and the factors of 27 are 1, 3, 9, 27. The greatest common factor is 9.

The largest number that can divide both 45 and 60 is the HCF of 45 and 60. The factors of 45 are 1, 3, 5, 9, 15, 45 and the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The greatest common factor is 15.

The HCF of 11 and 13 is the largest number that divides both of them without leaving a remainder. Since 11 and 13 are both prime numbers, the only common factor is 1.

The HCF of 33 and 44 is the largest number that divides both of them without leaving a remainder. The factors of 33 are 1, 3, 11, 33 and the factors of 44 are 1, 2, 4, 11, 22, 44. The greatest common factor is 11.