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My confusion was that like we know if we want to find the weight of a 51 kg person we would simply multiply it with 10(approx) and get 510 N.If we have 51 lbm and want to convert it into lbf then we can't simply multiply it with 32.2(approx) and get the answer but we will also have to take that 'g subscript c' into account which is also 32.2 and so these two 32.2s cancel out and we get 51lbf.

Am I right?