Lets break the question down into two smaller manageable parts. What is the highest common factor? : Common factor of two numbers is the largest number which perfectly divides both said numbers without any remainders. For example the numbers 18 and 24 are both perfectly divisible by the numbers 2,3 and 6. Therefore the highest common factor is 6. What is the lowest common multiple? Common multiple of two numbers is simply the smallest number which is perfectly divisible by the original two numbers. For example 18 and 24. We need to group the prime factors. I.e numbers only divisible by themselves. The number 18 can be written as (3 x 3 ) x (2). While the number 24 can be obtained by (2 x 2 x 2) x (3). There after selecting and multiplying the largest unique set of prime numbers from both 18 and 24 we obtain the largest common multiple. Therefore their largest common multiple is (3 x 3) x (2 x 2 x 2) or 72 which the smallest number to be perfectly divisible by both 18 and 24.