Question

MATHS - 10 POINTS HCF/LCM thankyou!!

A car’s service book states that the air filter must be replaced every 10,000 miles and the diesel fuel filter every 24,000 miles.

At how many miles will they both need replacing at the same time?

DO I WORK OUT THE LCM OR HCF?
WHAT IS THE FINAL ANSWER AND WHY??

PLEASE INCLUDE WORKING THANK YOUUU!!!!!

Answer 1

LCM

10,000|2
5,000|2
2,500|2
1,250|2
625|5
125|5
25|5
5|5
1

24,000|2
12,000|2
6,000|2
3,000|2
1,500|2
750|2
375|3
125|5
25|5
5|5
1


`LCM(10000,24000)=2^6\cdot3\cdot5^4=120,000`