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# what is the lowest common multiple of 2x3^2x5^4x7 and 750

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what is the lowest common multiple of 2x3^2x5^4x7 and 750

Dec 9, 2014

#1
+95177
+5

$$\\LCM \;of\;\;2\times3^2\times5^4\times7 \;\;and \;\;750\\\\ Well\; 750=3*250=3*2*5*5*5=2\times 3 \times 5^3$$

Lets look at these two

$$\\2 \times 3 \times 5^3\qquad \times \qquad 3\times 5\times 7\quad=\quad 2\times 3^2 \times 5^4\times 7\\\\ 750\qquad \qquad \quad \times \qquad 3\times 5\times 7\quad=\quad 2\times 3^2 \times 5^4\times 7\\\\$$

$$\\So\;\;750  is a factor of the  2\times 3^2 \times 5^4\times 7\\\\  So the lowest common multiple of these two is 2\times 3^2 \times 5^4\times 7$$

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Dec 9, 2014

#1
+95177
+5

$$\\LCM \;of\;\;2\times3^2\times5^4\times7 \;\;and \;\;750\\\\ Well\; 750=3*250=3*2*5*5*5=2\times 3 \times 5^3$$

Lets look at these two

$$\\2 \times 3 \times 5^3\qquad \times \qquad 3\times 5\times 7\quad=\quad 2\times 3^2 \times 5^4\times 7\\\\ 750\qquad \qquad \quad \times \qquad 3\times 5\times 7\quad=\quad 2\times 3^2 \times 5^4\times 7\\\\$$

$$\\So\;\;750  is a factor of the  2\times 3^2 \times 5^4\times 7\\\\  So the lowest common multiple of these two is 2\times 3^2 \times 5^4\times 7$$

Melody Dec 9, 2014