19 x 53
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5 & 23
Any pair of one even and one odd number will have an even product and an odd sum.
Pick any pair of prime numbers. 5, 7 11, 13 17, 19 Pick any pair of consecutive integers.
Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.
Any pair of prime numbers as for example 19 and 23