They have no common factors except 1, which goes into all numbers.
But 4, 5, 6, 7 do share a common multiple, a number they all go into. To find it we split the numbers into pairs. Take the even numbers first: 4 and 6 both go into 12. 4, 6 and 5 go into 5 × 12=60. And now we take 60 and 7 and multiply them together to give us 420. So 4, 5, 6 and 7 all go into 420.