Taking the two cons. evens to be 2n & 2n + 2, and using
product of two given numbers = their LCM x their gcf, we come up with
4n(n+1) = 120, or n(n+1) = 30, leading to n = 5. The two cons. even nos. in the question turn out to be 10 & 12.
The GCF of consecutive even numbers is 2. The LCM of consecutive even numbers is their product divided by 2.
Their GCF will be 2. Their LCM will be half their product.
54 and 56
The two numbers are 10 and 12.
Since the numbers differ by 2 and the GCF is 2, they are consecutive even integers. So the numbers are 6 and 8.
The LCM of two consecutive even numbers is their product divided by two.
Any consecutive even numbers, like 38 and 40.
18 and 20
The LCM will never be less than the GCF of a set of numbers.
It's the way numbers work. Consider 32 and 33. Consecutive integers are relatively prime, that is, their GCF is 1. If two numbers have a GCF of 1, the LCM will be their product. 32 x 33 = 1056 1 (GCF) x 1056 (LCM) = 1056 2 x 528 = 1056 3 x 352 = 1056 4 x 264 = 1056 Notice the pattern. As the GCF increases, the LCM decreases. Consider 32 and 34. Consecutive even numbers have a GCF of 2. The LCM of 32 and 34 is 544. 32 x 34 = 1088 2 (GCF) x 544 (LCM) = 1088 If you know either the GCF or the LCM of two numbers, you can find the other one without factoring again. The GCF of 28 and 36 is 4. Their product is 1008. Their LCM is 1008 divided by 4, or 252.
The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.
The product of the GCF and the LCM is the same as the product of the original two numbers. Divide the product of the original numbers by the GCF. The result will be the LCM.