The solution to lcm 30,42 is 210

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Find the LCM 30 , 42

Solution

lcm

30, 42

210

Solution steps

30, 42

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Prime factorization of

42 : 2 \cdot 3 \cdot 7

42

42

divides by

242 = 21 \cdot 2

= 2 \cdot 21

21

divides by

321 = 7 \cdot 3

= 2 \cdot 3 \cdot 7

2, 3, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 7

Multiply each factor the greatest number of times it occurs in either

30

42

= 2 \cdot 3 \cdot 5 \cdot 7

Multiply the numbers:

2 \cdot 3 \cdot 5 \cdot 7 = 210

= 210

\frac{126}{9}

\frac{15.5}{5}

18 x, 15

28 - 15

63, 45, 81