The lowest common multiple is found by multiplying all the factors which appear in either list:
So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.
900 = 2 x 2 x 3 x 3 x 5 x 5
270 = ___2 x 3 x 3 x 3 x 5
The coloured numbers are counted once only as they appear in both columns and don't need to be counted twice. Anything left over [the bold black numbers] are also included in the count.
So:
So:
2 x 2 x 3 x 3 x 3 x 5 x 5 = 2700 the LCM is 2700. OK?
Now try these: 63,28; 70,64; 147,45; 175, 120
Answers below
252, 2240, 4410, 4200
The LCM (of 2 integers, A and B) is also given by the product of the two numbers divided by their greatest common factor (GCF). Sometimes, it can be be a little quicker to calculate the LCM that way, and it is, anyway, an interesting relation.
ReplyDeleteFor example, with 175 and 120, one (or at least I) can see quickly that 175 is 7x25, neither of which have 2 or 3 as factors; likewise, 120 is 12x10, neither of which have 7 as a factor. So 5 is the only common prime factor; it occurs only once in 10 (though twice in 25), so the GCF of 175 and 120 is 5; accordingly, the LCM is 175x120/5 (=4,200).
Best regards
That's a bit professional for poor amateurs like me but I'll try it, Nigel.
ReplyDeleteNot good with maths :-/
ReplyDeleteCan't do that - it's maths!
ReplyDelete