A new vintage 1965 convertible requires an oil change every 2 comma 500 miles and replacement of all fluids every 19 comma 000 miles. If these services have just been performed by the dealer, how many miles from now will both be due at the same time?

Let x be the number of miles traveled by the convertible by the time that both services be due at the same time. Since by that time several services of a change of the oil and change of the fluids have done then x must the first common multiple of 2,500 and 19,000, in other words, x is the least common multiple. Using prime factorization:

[tex]2,500=5^4*2^2[/tex]

[tex]19,000=19*5^3*2^3[/tex]

To get the value of the least common multiple, you have to multiply each prime with the highest exponent:

[tex]x=lcm(2500,19000)=19^1*5^4*2^3=95000[/tex]

A new vintage 1965 convertible requires an oil change every 2 comma 500 miles and replacement of all fluids every 19 comma 000 miles. If these services have just been performed by the​ dealer, how many miles from now will both be due at the same​ time?

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A new vintage 1965 convertible requires an oil change every 2 comma 500 miles and replacement of all fluids every 19 comma 000 miles. If these services have just been performed by the dealer, how many miles from now will both be due at the same time?