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Find the LCM of: 294, 420 and 504.

Answer
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Hint: To find the LCM of the number first express the number into their products of prime numbers, then take the prime number with the highest power.

Complete step by step answer:
 First, find the prime factors of 294.
The prime factor of 294 is given below:
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Express 294 as a product of their prime factors,
294=2×3×7×7294=2×3×72 …… (1)

Now, find the prime factors of 420.
The prime factor of 420 is given below:
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Express 420 as a product of their prime factors,
420=2×2×3×5×7420=22×3×5×7 …… (2)

Now, find the prime factors of 504.
The prime factor of 504 is given below:
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Express 504 as a product of their prime factors,
504=2×2×2×3×3×7504=23×32×7 …… (3)
Now, from (1), (2) and (3) choose the prime number with greatest power and multiply them.
Therefore,
LCM=23×32×5×72LCM=8×9×5×49LCM=17640

Note: While choosing the prime numbers with greatest power make sure to choose every prime number even if some of it have power only one.
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