Finding least common multiples. (Picture)

Question

Picture: https://imgur.com/BlYqh1U

This problem is wanting me to use a certain formula that I am new to. Could anyone show me how to work these out?

Problems and numbers are in picture. Thank you for any help.

Answer 1

a=54, b=12

a= 2(3³)   b=2³(3)   so GCD of a,b is 2(3), i.e. 6

 

Using the formula that LCM(a.b) = ab / [GCD(a,b)]

we get LCM = (54) (12)/ 6 = =108.

Answer 2

54 and 12:

 

Prime factors of:

   54 = 2*3*3*3

   12 = 2*2*3

 

LCM (54,12) = 54 * 12 / GCD(54,12)

                   = 2*3*3*3 * 2*2*3 / (2*3)

                   = 2*2*3*3*3

                   =  108

 

 

884 and 299:

 

Prime factors of:

   884 = 2*2*13*17

   299 = 13*23

 

LCM(884,299) = 884*299 / GCD(884,299)

              = 2*2*13*17 * 13*23  /  13

              = 2*2*13*17*23

              = 20332

Answer 3

if a and b are two numbers, the formula means...

axb=LCM*GCF

the product of the two numbers equals the product of the LCM and GCF

therefore LCM=axb/GCF

example:

12 and 18: GCF=6 and LCM=36, 6*36=12*18, 216=216

1) 54 and 12

the GCF is 6, therefore (54*12)/6=LCM, simplify or multiply, 648/6=108=LCM

doing it the other way...

54=2*3*3*3

12=2*2*3

LCM=2*3*3*3*2=108

 

2) 884 and 299

find the GCF by first factoring the numbers as products of prime factors

884=2*442=2*2*221=2*2*13*17

299=13*23

GCF=13

(884*299)/13=264,316/13=20,332=LCM

doing it the other way...

LCM=2*2*13*17*23=20,332