what is the lcm of 16 and 24?

LCM = 48

Here's why

16 = 4•4, 24 = 4•6

24 has three 2s and one 3 as prime factor
16 has four 2s and NO 3s.

So add a factor of 3 to the 16 and get 3•16 = 48.
Alternately you can add the missing 2 to 24 and get 2•24 = 48.

Either way works. You have to have at least four 2s and one 3.

Note 16 goes into 48 3 times
24 goes into 48 2 times as they should.

2

16___32___48___64_____>Multiples of 16
24___48___72___96_____>Multiples of 24

LCM = 48

48

Method 1 Factors
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
Take common factors = 2 × 2 × 2 = 8 -------- GCD
Take un common factors = 2 × 3 = 6
LCM = GCD × un common factors = 8 × 6 = 48

Method 2 combined factors
2| 16 | 24 ---------- common factor
2| 08 | 12 ---------- common factor
2 | 04 | 06 ---------- common factor
2 | 02 | 03 ---------- uncommon factor
3 | 01 | 03 ---------- uncommon factor
--| 01 | 01

LCM = 2 × 2 × 2 × 2 × 3 = 48
-----

LCM is least common multiple
so the lowest number that BOTH 16 and 24 go into
multiples of 16: 16, 32, 48, 64, 80 (I'm going to stop there)
multiples of 24: 24, 48 (I'm going to stop here because theres a matching number)

so the LCM of 16 and 24 is 48! :)

hope this helps ;)

Prime factors of 16 = 2*2*2*2
Prime factors of 24 = 2*2*2*3
L.C.M. = 2*2*2*2*3 = 48

48

Cause 16x3=48 and 24x2=48

16 = 2^4
24 = 2^3 x 3
---------------------
.....= 2^4 x 3
.....= 48

48