No.
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The LCM is 216.
1080
27 cannot be a multiple of 4 because 27 is an odd number and 4 is an even number. No odd number can be a multiple of an even number, only even numbers can be multiples of even numbers.
LCM of 27 & 5 = 27 x 5 = 135. LCM of a prime number and a composite number is equal to their product if the composite number is not a multiple of the prime number.
The least common multiple of 14 and 27 is 378