Question

1. find the lcm.

(1) (2, 6, 18) → □
(2) (4, 6, 18) → □
(3) (5, 9, 18) → □
(4) (6, 9, 18) → □
(5) (2, 13, 26) → □
(6) (7, 8, 28) → □
(7) (7, 9, 21) → □
(8) (6, 9, 27) → □
(9) (9, 15, 30) → □
(10) (8, 12, 36) → □

Explanation:

Step1: Prime factorize all numbers

For each set:
(2) $4=2^2$, $6=2\times3$, $18=2\times3^2$
(3) $5=5$, $9=3^2$, $18=2\times3^2$
(4) $6=2\times3$, $9=3^2$, $18=2\times3^2$
(5) $2=2$, $13=13$, $26=2\times13$
(6) $7=7$, $8=2^3$, $28=2^2\times7$
(7) $7=7$, $9=3^2$, $21=3\times7$
(8) $6=2\times3$, $9=3^2$, $27=3^3$
(9) $9=3^2$, $15=3\times5$, $30=2\times3\times5$
(10) $8=2^3$, $12=2^2\times3$, $36=2^2\times3^2$

Step2: Take max exponents of primes

(2) $\text{LCM}=2^2\times3^2=36$
(3) $\text{LCM}=2\times3^2\times5=90$
(4) $\text{LCM}=2\times3^2=18$
(5) $\text{LCM}=2\times13=26$
(6) $\text{LCM}=2^3\times7=56$
(7) $\text{LCM}=3^2\times7=63$
(8) $\text{LCM}=2\times3^3=54$
(9) $\text{LCM}=2\times3^2\times5=90$
(10) $\text{LCM}=2^3\times3^2=72$

Answer:

(2) 36
(3) 90
(4) 18
(5) 26
(6) 56
(7) 63
(8) 54
(9) 90
(10) 72