Question

How many numbers between 300 and 600 are divisible by 4,5,6?

Answer 1

To be divisible by 4,5, and 6, a number must be a multiple of their least common multiple. So we find the least common multiple,

LCM: 4 = 2·2,

LCM:5=5

LCM:6=2.3

LCM = 2·2·3·5 = 60 So each number must be a multiple of 60. so any number which is multiple to 60 is 300.we know a+(n-1)d=Tn.a=300.d=60.Tn=600.So answer will be 6.Hence there are 6 numbers divisible by 4,5,6