Answer:
(a) 144
(b) 117
(c) 360
(d) 588
(e) 5472
Step-by-step explanation:
To find the LCM of two numbers, first find the prime factorization of each number. Then the LCM is the product of common and not common factors with the larger exponent.
2.
(a)
[tex]72 = 2^3 \times 3^2[/tex]
[tex]144 = 2^4 \times 3^2[/tex]
[tex]LCM = 2^4 \times 3^2 = 8 \times 9 = 144[/tex]
(b)
[tex]39 = 3 \times 13[/tex]
[tex]117 = 3^2 \times 13[/tex]
[tex]LCM = 3^2 \times 13 = 117[/tex]
(c)
[tex]72 = 2^3 \times 3^2[/tex]
[tex]90 = 2 \times 3^2 \times 5[/tex]
[tex]LCM = 2^3 \times 3^2 \times 5 = 360[/tex]
(d)
[tex]84 = 2^2 \times 3 \times 7[/tex]
[tex]147 = 3 \times 7^2[/tex]
[tex]LCM = 2^2 \times 3 \times 7^2 = 588[/tex]
(e)
[tex]152 = 2^3 \times 19[/tex]
[tex]288 = 2^5 \times 3^2[/tex]
[tex]LCM = 2^5 \times 3^2 \times 19 = 5472[/tex]
